{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 用户和活动关联关系处理\n",
    "\n",
    "\n",
    "整个数据集中活动数目（events.csv）太多，所以下面的处理我们找出只在训练集和测试集中出现的活动和用户集合，并对他们重新编制索引"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#保存数据\n",
    "import pickle\n",
    "\n",
    "import itertools\n",
    "\n",
    "#处理事件字符串\n",
    "import datetime\n",
    "\n",
    "import numpy as np\n",
    "import scipy.io as sio #文件输入输出\n",
    "import scipy.sparse as ss #稀疏矩阵\n",
    "\n",
    "#相似度/距离\n",
    "import scipy.spatial.distance as ssd\n",
    "\n",
    "from collections import defaultdict\n",
    "from sklearn.preprocessing import normalize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of uniqueUsers :3391\n",
      "number of uniqueEvents :13418\n"
     ]
    }
   ],
   "source": [
    " \"\"\"\n",
    "我们只关心train和test中出现的user和event，因此重点处理这部分关联数据\n",
    "\n",
    "train.csv 有6列：\n",
    "user：用户ID\n",
    "event：活动ID\n",
    "invited：是否被邀请（0/1）\n",
    "timestamp：ISO-8601 UTC格式时间字符串，表示用户看到该活动的时间\n",
    "interested, and not_interested\n",
    "\n",
    "Test.csv 除了没有interested, and not_interested，其余列与train相同\n",
    " \"\"\"\n",
    "    \n",
    "# 统计训练集中有多少不同的用户的events\n",
    "uniqueUsers = set() #用户数目\n",
    "uniqueEvents = set() #event num\n",
    "\n",
    "#倒排表\n",
    "#统计每个用户参加的活动   / 每个活动参加的用户\n",
    "eventsForUser = defaultdict(set)\n",
    "usersForEvent = defaultdict(set)\n",
    "    \n",
    "for filename in [\"train.csv\", \"test.csv\"]:\n",
    "    f = open(\"./data/\"+filename, 'r')\n",
    "    #忽略第一行（列名字）\n",
    "    f.readline().strip().split(\",\")\n",
    "    \n",
    "    for line in f:    #对每条记录\n",
    "        cols = line.strip().split(\",\")\n",
    "        uniqueUsers.add(cols[0])   #第一列为用户ID\n",
    "        uniqueEvents.add(cols[1])   #第二列为活动ID\n",
    "        \n",
    "        #eventsForUser[cols[0]].add(cols[1])    #该用户参加了这个活动\n",
    "        #usersForEvent[cols[1]].add(cols[0])    #该活动被用户参加\n",
    "    f.close()\n",
    "\n",
    "\n",
    "n_uniqueUsers = len(uniqueUsers)\n",
    "n_uniqueEvents = len(uniqueEvents)\n",
    "\n",
    "print(\"number of uniqueUsers :%d\" % n_uniqueUsers)\n",
    "print(\"number of uniqueEvents :%d\" % n_uniqueEvents)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#用户关系矩阵表，可用于后续LFM/SVD++处理的输入\n",
    "#这是一个稀疏矩阵，记录用户对活动感兴趣\n",
    "userEventScores = ss.dok_matrix((n_uniqueUsers, n_uniqueEvents))\n",
    "userIndex = dict()\n",
    "eventIndex = dict()\n",
    "\n",
    "#重新编码用户索引字典\n",
    "for i, u in enumerate(uniqueUsers):\n",
    "    userIndex[u] = i #用户索引词典\n",
    "    \n",
    "#重新编码活动索引字典    \n",
    "for i, e in enumerate(uniqueEvents):\n",
    "    eventIndex[e] = i #活动索引词典\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_records = 0\n",
    "ftrain = open(\"./data/train.csv\", 'r')\n",
    "ftrain.readline()\n",
    "for line in ftrain:\n",
    "    cols = line.strip().split(\",\")\n",
    "    i = userIndex[cols[0]]  #用户\n",
    "    j = eventIndex[cols[1]] #活动\n",
    "    \n",
    "    eventsForUser[i].add(j)    #该用户参加了这个活动\n",
    "    usersForEvent[j].add(i)    #该活动被用户参加\n",
    "        \n",
    "    #userEventScores[i, j] = int(cols[4]) - int(cols[5])   #interested - not_interested\n",
    "    score = int(cols[4]) #是否感兴趣\n",
    "    #if score == 0:  #0在稀疏矩阵中表示该元素不存在，因此借用-1表示interested=0\n",
    "    #userEventScores[i, j] = -1\n",
    "    #else:\n",
    "    userEventScores[i, j] = score #代表用户I对这个活动是否感兴趣\n",
    "ftrain.close()\n",
    "\n",
    "  \n",
    "##统计每个用户参加的活动，后续用于将用户朋友参加的活动影响到用户\n",
    "pickle.dump(eventsForUser, open(\"PE_eventsForUser.pkl\", 'wb'))\n",
    "##统计活动参加的用户\n",
    "pickle.dump(usersForEvent, open(\"PE_usersForEvent.pkl\", 'wb'))\n",
    "\n",
    "#保存用户-活动关系矩阵R，以备后用\n",
    "sio.mmwrite(\"PE_userEventScores\", userEventScores)\n",
    "\n",
    "\n",
    "#保存用户索引表\n",
    "pickle.dump(userIndex, open(\"PE_userIndex.pkl\", 'wb'))\n",
    "#保存活动索引表\n",
    "pickle.dump(eventIndex, open(\"PE_eventIndex.pkl\", 'wb'))\n",
    "\n",
    "    \n",
    "# 为了防止不必要的计算，我们找出来所有关联的用户 或者 关联的event\n",
    "# 所谓的关联用户，指的是至少在同一个event上有行为的用户pair\n",
    "# 关联的event指的是至少同一个user有行为的event pair\n",
    "uniqueUserPairs = set()\n",
    "uniqueEventPairs = set()\n",
    "for event in uniqueEvents:\n",
    "    i = eventIndex[event]\n",
    "    users = usersForEvent[i]\n",
    "    if len(users) > 2:\n",
    "        uniqueUserPairs.update(itertools.combinations(users, 2))\n",
    "        \n",
    "for user in uniqueUsers:\n",
    "    u = userIndex[user]\n",
    "    events = eventsForUser[u]\n",
    "    if len(events) > 2:\n",
    "        uniqueEventPairs.update(itertools.combinations(events, 2))\n",
    " \n",
    "#保存用户-事件关系对索引表\n",
    "pickle.dump(uniqueUserPairs, open(\"FE_uniqueUserPairs.pkl\", 'wb'))\n",
    "pickle.dump(uniqueEventPairs, open(\"PE_uniqueEventPairs.pkl\", 'wb'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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       " '1805653308': 934,\n",
       " '3316715342': 935,\n",
       " '2271406145': 936,\n",
       " '160230482': 937,\n",
       " '1524886161': 938,\n",
       " '441103517': 939,\n",
       " '1832146052': 940,\n",
       " '2054648409': 941,\n",
       " '2583651606': 942,\n",
       " '3042642967': 943,\n",
       " '4081921627': 944,\n",
       " '146035325': 945,\n",
       " '738525400': 946,\n",
       " '1462567031': 947,\n",
       " '4072712031': 948,\n",
       " '2122304529': 949,\n",
       " '1520557068': 950,\n",
       " '1956869615': 951,\n",
       " '3269471699': 952,\n",
       " '1016099896': 953,\n",
       " '2124468398': 954,\n",
       " '3715650761': 955,\n",
       " '3480781792': 956,\n",
       " '3041705231': 957,\n",
       " '4026562594': 958,\n",
       " '2645338549': 959,\n",
       " '4162525077': 960,\n",
       " '3941958556': 961,\n",
       " '457456094': 962,\n",
       " '546007936': 963,\n",
       " '3815746762': 964,\n",
       " '1071963586': 965,\n",
       " '1115995297': 966,\n",
       " '540360566': 967,\n",
       " '2837984655': 968,\n",
       " '419778061': 969,\n",
       " '2070073073': 970,\n",
       " '320000323': 971,\n",
       " '1784981569': 972,\n",
       " '1112792616': 973,\n",
       " '2238460219': 974,\n",
       " '1851530247': 975,\n",
       " '719203242': 976,\n",
       " '1876906939': 977,\n",
       " '988874074': 978,\n",
       " '2541238114': 979,\n",
       " '881544435': 980,\n",
       " '1931818423': 981,\n",
       " '3471761709': 982,\n",
       " '1020875748': 983,\n",
       " '4018723397': 984,\n",
       " '2877985693': 985,\n",
       " '3556981605': 986,\n",
       " '2334852679': 987,\n",
       " '2490592488': 988,\n",
       " '3375265240': 989,\n",
       " '160673392': 990,\n",
       " '3581835660': 991,\n",
       " '3408163802': 992,\n",
       " '487468823': 993,\n",
       " '256035140': 994,\n",
       " '765240064': 995,\n",
       " '4195841083': 996,\n",
       " '1290399197': 997,\n",
       " '3044948713': 998,\n",
       " '3165928866': 999,\n",
       " ...}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "userIndex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defaultdict(set,\n",
       "            {1546: {2732, 4091, 4448, 8190, 10434, 12841},\n",
       "             1544: {1371, 2602, 4297, 5270, 5535, 7419, 11584},\n",
       "             2001: {1594, 5031, 7533, 7951, 9907, 12469},\n",
       "             703: {797, 2559, 4283, 7252, 7638, 12694},\n",
       "             2923: {7512, 7670, 9338, 9889, 10259, 13197},\n",
       "             911: {40,\n",
       "              305,\n",
       "              952,\n",
       "              1896,\n",
       "              2266,\n",
       "              4492,\n",
       "              6263,\n",
       "              6840,\n",
       "              7071,\n",
       "              7857,\n",
       "              8012,\n",
       "              12416,\n",
       "              12590,\n",
       "              13212},\n",
       "             2818: {1855, 4466, 7703, 8850, 9204, 11773},\n",
       "             3279: {1896, 2689, 2701, 8214, 9736, 12586},\n",
       "             555: {918, 1126, 2335, 6918, 10199, 12123, 12593},\n",
       "             2838: {4524, 5515, 5545, 8926, 11529, 12483},\n",
       "             201: {143, 355, 1745, 9195, 11236, 12870},\n",
       "             429: {1871, 2200, 2527, 2983, 10122, 12304},\n",
       "             3323: {1773, 3278, 3577, 6077, 10445, 12031},\n",
       "             3007: {56,\n",
       "              1785,\n",
       "              1896,\n",
       "              2431,\n",
       "              4448,\n",
       "              4962,\n",
       "              5972,\n",
       "              6570,\n",
       "              7190,\n",
       "              8190,\n",
       "              9051,\n",
       "              9318,\n",
       "              10434,\n",
       "              10500,\n",
       "              11189,\n",
       "              11251,\n",
       "              11625,\n",
       "              12122,\n",
       "              12277,\n",
       "              12500,\n",
       "              13059},\n",
       "             719: {5936, 7888, 8559, 10929, 12968, 13083},\n",
       "             2159: {355, 1896, 4448, 7190, 7284, 8190, 10434, 12500, 13333},\n",
       "             1759: {957, 1047, 3202, 5757, 10054},\n",
       "             572: {2978, 4422, 6785, 9370, 9583, 12886},\n",
       "             1376: {3129, 7012, 9018, 10322, 12911},\n",
       "             2916: {781, 1579, 5983, 6118, 11160, 12126},\n",
       "             1812: {2038, 3407, 4790, 7176, 8223, 10949},\n",
       "             2870: {1896, 2431, 4448, 6415, 7190, 8190, 10434, 10500},\n",
       "             2218: {1751, 3288, 6900, 7143, 10704, 12285, 13189},\n",
       "             2010: {1985, 2125, 3852, 7860, 9126, 11140},\n",
       "             1872: {1011, 1371, 6630, 8711, 10231, 11584},\n",
       "             378: {2038, 4407, 5414, 6468, 8200, 12187},\n",
       "             681: {3972, 6028, 6754, 8072, 11400, 11631},\n",
       "             443: {2239, 2287, 2341, 4277, 7650, 10173},\n",
       "             2490: {4263, 5655, 5697, 9606, 9653, 9958, 12455},\n",
       "             1277: {377, 3107, 4227, 4444, 4674, 6044, 9125},\n",
       "             2374: {1896, 5318, 6298, 6725, 6814, 6948, 7190, 12436},\n",
       "             646: {5, 955, 1672, 2916, 3762, 4301, 5456},\n",
       "             720: {4745, 5414, 10624, 12423},\n",
       "             2064: {1794,\n",
       "              1998,\n",
       "              3259,\n",
       "              5029,\n",
       "              5119,\n",
       "              6144,\n",
       "              9651,\n",
       "              10990,\n",
       "              11559,\n",
       "              12884},\n",
       "             3129: {897,\n",
       "              2367,\n",
       "              5546,\n",
       "              5830,\n",
       "              8212,\n",
       "              8587,\n",
       "              8870,\n",
       "              8989,\n",
       "              9567,\n",
       "              10279,\n",
       "              11214,\n",
       "              11462},\n",
       "             2020: {1011, 1371, 3436, 9439, 11831, 11924},\n",
       "             2449: {5128, 7070, 7923, 10572, 11714, 12776},\n",
       "             653: {1268, 1289, 1896, 4448, 6578, 8190, 10434, 12531, 13333},\n",
       "             1002: {4735, 7697, 7742, 8876, 9330, 10405},\n",
       "             844: {828, 1964, 3391, 9751, 10311, 11381, 11947, 12707, 13246},\n",
       "             613: {132, 3107, 3157, 4000, 4674, 8320, 10173},\n",
       "             103: {3907, 5092, 8244, 9365, 9859, 12410},\n",
       "             117: {457, 564, 4071, 4407, 10996, 12411, 12593},\n",
       "             1490: {2126, 2584, 2952, 3223, 4620, 7685, 9075},\n",
       "             2722: {253,\n",
       "              4109,\n",
       "              4587,\n",
       "              8530,\n",
       "              9445,\n",
       "              9932,\n",
       "              11207,\n",
       "              11663,\n",
       "              12051,\n",
       "              12414,\n",
       "              12471,\n",
       "              13158},\n",
       "             3003: {802,\n",
       "              4071,\n",
       "              4312,\n",
       "              4407,\n",
       "              5448,\n",
       "              5757,\n",
       "              6713,\n",
       "              8016,\n",
       "              9633,\n",
       "              9822,\n",
       "              9829,\n",
       "              11263,\n",
       "              12452},\n",
       "             2278: {13, 41, 8039, 8200, 8494, 9382, 12234},\n",
       "             1408: {60, 2063, 5923, 6666, 9261, 13037},\n",
       "             1995: {259, 5748, 9487, 9595, 10614, 12363},\n",
       "             1873: {3871, 6318, 7071, 8190, 12590, 13356},\n",
       "             1473: {863, 1130, 4403, 5725},\n",
       "             2998: {445,\n",
       "              1896,\n",
       "              3246,\n",
       "              3921,\n",
       "              4448,\n",
       "              5409,\n",
       "              6765,\n",
       "              7190,\n",
       "              7196,\n",
       "              8190,\n",
       "              8663,\n",
       "              8738,\n",
       "              9005,\n",
       "              10434,\n",
       "              12489,\n",
       "              12500,\n",
       "              13333,\n",
       "              13379},\n",
       "             2039: {109,\n",
       "              1038,\n",
       "              1109,\n",
       "              1464,\n",
       "              2294,\n",
       "              2549,\n",
       "              2942,\n",
       "              3423,\n",
       "              3494,\n",
       "              4474,\n",
       "              4642,\n",
       "              4970,\n",
       "              5013,\n",
       "              5203,\n",
       "              5634,\n",
       "              6214,\n",
       "              8367,\n",
       "              8440,\n",
       "              8838,\n",
       "              10255,\n",
       "              10276,\n",
       "              10452,\n",
       "              11388,\n",
       "              11549,\n",
       "              11842,\n",
       "              11874,\n",
       "              12791,\n",
       "              12965,\n",
       "              13046},\n",
       "             423: {925, 1854, 2038, 3783, 10607, 10886},\n",
       "             2735: {579, 3427, 7376, 7739, 8756, 11248},\n",
       "             492: {1126, 3228, 4407, 8200, 12490},\n",
       "             1882: {3141, 5167, 6984, 7899, 10535, 11325, 11533},\n",
       "             2549: {1783, 4313, 6300, 9514, 11002, 13188},\n",
       "             3082: {3846, 6222, 6783, 9040, 9085, 10264},\n",
       "             2641: {1896, 4838, 7190, 8190, 8726, 10434, 12277, 13333},\n",
       "             3046: {56,\n",
       "              1896,\n",
       "              6859,\n",
       "              7190,\n",
       "              7479,\n",
       "              7754,\n",
       "              8090,\n",
       "              8190,\n",
       "              10300,\n",
       "              13252},\n",
       "             716: {1855, 3751, 5448, 8587, 10890, 10962, 11870, 13215},\n",
       "             1522: {2850, 3330, 4473, 5808, 6019, 9762, 12259},\n",
       "             1611: {1812, 3503, 3710, 4407, 6468, 11802, 12571},\n",
       "             1060: {12, 3240, 5604, 5833, 10895, 11142, 13221},\n",
       "             773: {1896, 4452, 6725, 7190, 8190, 10353},\n",
       "             2530: {1365,\n",
       "              2641,\n",
       "              8217,\n",
       "              9482,\n",
       "              9991,\n",
       "              10787,\n",
       "              12330,\n",
       "              12436,\n",
       "              13130,\n",
       "              13237},\n",
       "             2789: {224, 1715, 3157, 4000, 4674, 8779, 10173},\n",
       "             1200: {1011, 1371, 5534, 6630, 7801, 11924},\n",
       "             2493: {4537, 5313, 6605, 7803, 8441, 10644, 12772},\n",
       "             2420: {660, 1200, 1262, 6976, 7883, 11154},\n",
       "             1142: {4424, 9139, 9383, 11909},\n",
       "             3305: {4490,\n",
       "              5437,\n",
       "              6051,\n",
       "              6137,\n",
       "              6352,\n",
       "              6658,\n",
       "              7254,\n",
       "              8804,\n",
       "              10004,\n",
       "              11737,\n",
       "              12540,\n",
       "              13137},\n",
       "             2267: {2672, 4934, 6720, 9677, 12326, 12593},\n",
       "             2753: {945, 2493, 5694, 9217, 11128, 12452},\n",
       "             3354: {2660, 3107, 4674, 7039, 9125, 13274},\n",
       "             3018: {1130, 1896, 1899, 3334, 7190, 8190, 11170},\n",
       "             864: {1371, 4293, 4297, 8711, 9439, 10077},\n",
       "             319: {1583, 2358, 4089, 4312, 4407, 8016, 10612, 11882},\n",
       "             2114: {346, 957, 7887, 9616, 12689},\n",
       "             915: {4880, 6288, 7268, 10234, 11752, 12646},\n",
       "             154: {103,\n",
       "              1410,\n",
       "              3335,\n",
       "              3380,\n",
       "              3825,\n",
       "              4448,\n",
       "              4929,\n",
       "              5145,\n",
       "              10434,\n",
       "              10500,\n",
       "              10593,\n",
       "              10838},\n",
       "             1480: {1439, 3946, 5262, 10876, 10983, 12842},\n",
       "             3163: {232, 5318, 5607, 5918, 6902, 11291, 13244},\n",
       "             2934: {2578, 3334, 5501, 6567, 6854, 9313},\n",
       "             827: {2465, 2727, 6127, 7078, 8411, 10004},\n",
       "             2181: {3533, 8615, 8772, 9604, 11334, 11357, 12860, 13261},\n",
       "             515: {710,\n",
       "              864,\n",
       "              875,\n",
       "              2525,\n",
       "              3202,\n",
       "              3897,\n",
       "              4375,\n",
       "              6111,\n",
       "              7474,\n",
       "              8387,\n",
       "              10351,\n",
       "              11225,\n",
       "              11455},\n",
       "             2085: {1896, 7190, 8190, 8462, 8961, 12041},\n",
       "             2052: {20, 2630, 2933, 3145, 3352, 9114},\n",
       "             1719: {1240, 2660, 3446, 4377, 4674, 8779, 10173},\n",
       "             175: {1508, 3346, 7752, 11982, 12568},\n",
       "             1405: {656, 1679, 4844, 6566, 12891, 13045},\n",
       "             1292: {127, 3237, 3280, 3420, 9912, 11435},\n",
       "             194: {1302, 1896, 5546, 8974, 10038, 10339, 12330, 12554},\n",
       "             608: {1085, 1946, 3527, 7180, 8527, 9416},\n",
       "             1041: {3407, 5286, 5709, 7218, 10197, 12230, 12485},\n",
       "             858: {1896, 2657, 4448, 8190, 10434, 10500, 12384},\n",
       "             2137: {56,\n",
       "              865,\n",
       "              1896,\n",
       "              5429,\n",
       "              5854,\n",
       "              6578,\n",
       "              6579,\n",
       "              8190,\n",
       "              8777,\n",
       "              10527,\n",
       "              11063,\n",
       "              11170,\n",
       "              12294},\n",
       "             2380: {4002, 5428, 6362, 6562, 8015, 10532, 11752},\n",
       "             1073: {1513, 3013, 6688, 8287, 10718, 12868},\n",
       "             483: {381, 3905, 7866, 8058, 9642, 9674, 12423},\n",
       "             874: {4645, 5219, 6010, 6630, 8311, 10797, 11718, 12418},\n",
       "             2980: {2503, 5265, 9047, 10657, 12249, 13079},\n",
       "             1062: {175, 4534, 7066, 11187, 12290, 13393},\n",
       "             127: {288, 3286, 8173, 11163, 12711},\n",
       "             306: {1366,\n",
       "              1896,\n",
       "              2853,\n",
       "              3869,\n",
       "              4448,\n",
       "              4571,\n",
       "              4859,\n",
       "              7190,\n",
       "              8190,\n",
       "              10434,\n",
       "              12500,\n",
       "              12586,\n",
       "              13057},\n",
       "             455: {4407, 4506, 6258, 6544, 8200, 12012},\n",
       "             791: {937, 1800, 6094, 12757},\n",
       "             2416: {2359, 4407, 5414, 5573, 9133, 12239},\n",
       "             2977: {2660, 4000, 4674, 8779, 10173, 13274},\n",
       "             540: {4087, 8521, 9032, 9048, 9258, 9297, 11895, 13011},\n",
       "             2404: {1378, 6318, 6468, 8628, 9167, 11403},\n",
       "             2127: {1014, 10177, 10652, 11359, 12818},\n",
       "             210: {4293, 4297, 5535, 6181, 7287, 11345, 11584},\n",
       "             392: {1896, 3871, 6318, 7071, 8190, 11403},\n",
       "             2858: {795, 1230, 5448, 8651, 9829, 9961},\n",
       "             1320: {1025, 1975, 5537, 5919, 7509, 10705, 10768, 12659},\n",
       "             2531: {651, 1544, 2318, 2755, 9503, 11336},\n",
       "             2529: {132, 3107, 4599, 4674, 6343, 9125},\n",
       "             1493: {380,\n",
       "              488,\n",
       "              1010,\n",
       "              2366,\n",
       "              4179,\n",
       "              5917,\n",
       "              6211,\n",
       "              6223,\n",
       "              6402,\n",
       "              7853,\n",
       "              9073,\n",
       "              9689,\n",
       "              9840,\n",
       "              10391,\n",
       "              10700,\n",
       "              11125,\n",
       "              12040},\n",
       "             34: {7240, 11882, 12007, 12645, 12765},\n",
       "             2211: {1855, 2214, 6263, 9487, 10962, 12690},\n",
       "             2516: {3434, 3716, 5873, 6563, 6874, 11937},\n",
       "             1430: {3341, 3570, 5639, 6558, 12542, 13292},\n",
       "             3295: {4967, 6318, 7071, 11403, 13087, 13212, 13356},\n",
       "             2134: {1085,\n",
       "              1730,\n",
       "              2465,\n",
       "              2863,\n",
       "              4537,\n",
       "              6355,\n",
       "              6362,\n",
       "              6598,\n",
       "              7180,\n",
       "              7803,\n",
       "              12008,\n",
       "              12293,\n",
       "              12725},\n",
       "             1146: {910, 1899, 3334, 4181, 6578, 11868},\n",
       "             2658: {2696,\n",
       "              3065,\n",
       "              4454,\n",
       "              5497,\n",
       "              6357,\n",
       "              7274,\n",
       "              7717,\n",
       "              7756,\n",
       "              9221,\n",
       "              9720,\n",
       "              10563,\n",
       "              10694,\n",
       "              11052,\n",
       "              11390},\n",
       "             101: {72,\n",
       "              2156,\n",
       "              5114,\n",
       "              5464,\n",
       "              6269,\n",
       "              7300,\n",
       "              9430,\n",
       "              10015,\n",
       "              11144,\n",
       "              11534,\n",
       "              12588,\n",
       "              12593},\n",
       "             1498: {1222, 4227, 4674, 8779, 10173, 13274},\n",
       "             1627: {561, 5542, 8377, 10929, 11149, 12030},\n",
       "             1373: {500,\n",
       "              1817,\n",
       "              1896,\n",
       "              1947,\n",
       "              4406,\n",
       "              4448,\n",
       "              5042,\n",
       "              6545,\n",
       "              7190,\n",
       "              7772,\n",
       "              7835,\n",
       "              8190,\n",
       "              8462,\n",
       "              10434,\n",
       "              10500},\n",
       "             2336: {3,\n",
       "              403,\n",
       "              1318,\n",
       "              3128,\n",
       "              3359,\n",
       "              4862,\n",
       "              7584,\n",
       "              9798,\n",
       "              10509,\n",
       "              11686,\n",
       "              12590,\n",
       "              13166},\n",
       "             902: {224, 3107, 3446, 4674, 7353, 9125, 10173},\n",
       "             1775: {5072, 6721, 8773, 11268, 12192, 13249},\n",
       "             1698: {3251, 3386, 4597, 4962, 6644, 7190, 8961, 11251},\n",
       "             2836: {2343, 2922, 3478, 4625, 6204, 9098},\n",
       "             195: {1606,\n",
       "              1818,\n",
       "              2303,\n",
       "              2985,\n",
       "              3410,\n",
       "              3526,\n",
       "              4616,\n",
       "              4776,\n",
       "              5552,\n",
       "              7993,\n",
       "              8911,\n",
       "              8965,\n",
       "              9527,\n",
       "              9644,\n",
       "              9659,\n",
       "              9883,\n",
       "              10174,\n",
       "              11810,\n",
       "              11813,\n",
       "              12044},\n",
       "             3252: {377, 3107, 4674, 6188, 9069, 9125},\n",
       "             1338: {377, 2660, 4674, 7241, 8779, 10173},\n",
       "             472: {1476, 4001, 6634, 9843, 11692, 12089},\n",
       "             2092: {274, 795, 5448, 7819, 8390, 12354},\n",
       "             2487: {3340, 4748, 6166, 6799, 6977, 7430},\n",
       "             332: {658, 1585, 6951, 12452},\n",
       "             2926: {1656, 1896, 2571, 5546, 7190, 10518},\n",
       "             2776: {3440, 4786, 7615, 9097, 13143, 13191},\n",
       "             250: {3446, 4000, 4674, 6044, 7241, 7353},\n",
       "             1064: {2038, 4024, 4498, 5851, 7888, 8782, 10332, 13239, 13350},\n",
       "             1740: {2141, 2232, 2397, 3751, 3832, 4506, 4520, 7049},\n",
       "             3154: {2493, 3432, 3499, 3772, 5082, 11523},\n",
       "             1044: {837,\n",
       "              1896,\n",
       "              3871,\n",
       "              4928,\n",
       "              5318,\n",
       "              5607,\n",
       "              5844,\n",
       "              5866,\n",
       "              6298,\n",
       "              7190,\n",
       "              8190},\n",
       "             2917: {3107, 4674, 8779, 9125, 10173, 13274},\n",
       "             538: {3812, 4674, 7039, 7353, 8779, 10173},\n",
       "             1314: {1896, 4967, 5607, 12590, 12744},\n",
       "             742: {51, 1652, 3427, 3620, 8494, 9035, 11248, 12148},\n",
       "             1441: {3013, 5323, 8760, 8836, 9287, 13260},\n",
       "             1594: {213, 1443, 5351, 8972, 10411, 10420},\n",
       "             971: {1238, 1408, 4543, 9933, 11600, 13328},\n",
       "             2849: {2578, 3525, 3736, 4791, 12390, 12685},\n",
       "             176: {634, 2908, 5791, 6637, 9472, 12897},\n",
       "             2761: {1720, 2336, 4172, 8326, 8616, 10145, 12428},\n",
       "             2430: {1896,\n",
       "              3871,\n",
       "              4967,\n",
       "              5607,\n",
       "              7071,\n",
       "              7190,\n",
       "              7622,\n",
       "              8190,\n",
       "              10561,\n",
       "              13356},\n",
       "             1491: {3504, 4167, 4416, 9476, 9934, 10806},\n",
       "             2773: {132, 4000, 4599, 7353, 10169, 13274},\n",
       "             1543: {224, 3446, 4444, 4674, 6044, 10173},\n",
       "             3063: {2660, 3446, 4674, 7241, 8779, 10173},\n",
       "             1250: {1383, 1386, 1899, 4630, 7414, 11170, 12757},\n",
       "             3122: {1383,\n",
       "              2681,\n",
       "              5553,\n",
       "              6576,\n",
       "              7152,\n",
       "              7783,\n",
       "              9912,\n",
       "              10112,\n",
       "              10982,\n",
       "              11133},\n",
       "             3372: {256, 840, 1520, 1942, 12145, 12599, 13250},\n",
       "             2611: {49, 2391, 4469, 5585, 11246, 12384},\n",
       "             2397: {2299, 4990, 6626, 9522, 11538, 12264},\n",
       "             1745: {1896, 6318, 6830, 7190, 9167, 10561, 11371},\n",
       "             1641: {169, 280, 3074, 4118, 4451, 4481, 4792, 5364, 6827},\n",
       "             2419: {13, 2408, 3177, 6720, 8879, 9382},\n",
       "             3367: {1383, 1896, 4202, 7190, 7918, 12208},\n",
       "             2573: {5204, 8335, 8553, 9062, 9160, 10578, 11933, 12939},\n",
       "             2853: {1896,\n",
       "              2367,\n",
       "              3580,\n",
       "              4722,\n",
       "              5546,\n",
       "              5830,\n",
       "              10279,\n",
       "              10720,\n",
       "              11214,\n",
       "              13209},\n",
       "             3233: {802, 1217, 1583, 3201, 3224, 4312, 10929},\n",
       "             1052: {1361, 3464, 3707, 4795, 5130, 5449},\n",
       "             609: {346,\n",
       "              2536,\n",
       "              2879,\n",
       "              4615,\n",
       "              5565,\n",
       "              6311,\n",
       "              7153,\n",
       "              8713,\n",
       "              8992,\n",
       "              9217,\n",
       "              10424,\n",
       "              11063,\n",
       "              11598,\n",
       "              12459},\n",
       "             2619: {2442, 5869, 7867, 8583, 8617, 11230},\n",
       "             212: {1320, 2560, 3728, 5898, 9886, 10625},\n",
       "             2470: {4354,\n",
       "              5047,\n",
       "              5546,\n",
       "              6621,\n",
       "              7062,\n",
       "              7401,\n",
       "              7952,\n",
       "              10978,\n",
       "              11209,\n",
       "              11214},\n",
       "             1800: {1365, 3572, 3609, 6043, 6452, 7374, 11960, 12436, 13400},\n",
       "             657: {3450, 5313, 8441, 9416, 9784},\n",
       "             738: {322, 491, 2938, 4964, 7956, 12124},\n",
       "             2472: {1924, 3128, 3871, 5034, 5563, 6618, 7944},\n",
       "             557: {9063, 11883, 12252, 12389},\n",
       "             2527: {978, 3203, 4626, 6420, 6599, 7373, 11165, 11623},\n",
       "             3207: {346, 6830, 8200, 10038, 11093, 12593},\n",
       "             3227: {2573, 8081, 8176, 9578, 9824, 10005},\n",
       "             2378: {263, 4584, 5534, 8285, 8711, 9439, 9456},\n",
       "             2189: {1371, 4293, 6630, 7287, 9439, 11584},\n",
       "             3229: {361, 4163, 4245, 6162, 7004, 8409, 12253},\n",
       "             1648: {918, 3656, 4722, 6318, 8299, 11403},\n",
       "             3088: {1033,\n",
       "              2157,\n",
       "              2339,\n",
       "              2405,\n",
       "              5225,\n",
       "              6515,\n",
       "              7833,\n",
       "              9492,\n",
       "              10037,\n",
       "              12439},\n",
       "             2032: {918,\n",
       "              1094,\n",
       "              2306,\n",
       "              4008,\n",
       "              4942,\n",
       "              5414,\n",
       "              8792,\n",
       "              11119,\n",
       "              11357,\n",
       "              11870},\n",
       "             1910: {72, 6192, 8630, 8836, 9287, 9430},\n",
       "             798: {4101, 7247, 7265, 7416, 10968, 11636},\n",
       "             1147: {478,\n",
       "              2779,\n",
       "              3786,\n",
       "              3864,\n",
       "              4908,\n",
       "              5475,\n",
       "              6146,\n",
       "              6441,\n",
       "              7890,\n",
       "              8186,\n",
       "              8273,\n",
       "              8799,\n",
       "              9288,\n",
       "              10032,\n",
       "              11330,\n",
       "              11652,\n",
       "              11847,\n",
       "              12702,\n",
       "              12817},\n",
       "             333: {2660, 3446, 4674, 7039, 8779, 10173},\n",
       "             1100: {4549, 4595, 9090, 12355},\n",
       "             1956: {1896, 4448, 6149, 8190, 10434, 12532},\n",
       "             183: {377, 4227, 4674, 5166, 7353, 13274},\n",
       "             2829: {132, 1240, 2660, 3446, 4227, 4674, 13274},\n",
       "             1516: {132, 3107, 4227, 4444, 4674, 7042},\n",
       "             583: {560, 4450, 4619, 4846, 6458, 7019},\n",
       "             2482: {1439, 5262, 5671, 10412, 10634, 12673},\n",
       "             1148: {1321, 3602, 4832, 6457, 8972, 11922},\n",
       "             3195: {1198, 1959, 5928, 7018, 7447, 11590, 13371},\n",
       "             1339: {276,\n",
       "              919,\n",
       "              1217,\n",
       "              1789,\n",
       "              4951,\n",
       "              6848,\n",
       "              7218,\n",
       "              9640,\n",
       "              10601,\n",
       "              11594,\n",
       "              11683,\n",
       "              12230,\n",
       "              12485},\n",
       "             969: {56, 1896, 3384, 7190, 8190, 12755},\n",
       "             3216: {4282, 6577, 6911, 7308, 7802, 9209, 9253, 10929, 12026},\n",
       "             2424: {532, 1745, 1896, 2578, 3285, 3334},\n",
       "             3321: {589, 8281, 8448, 11835, 12469},\n",
       "             2517: {864, 3368, 7266, 9564, 10931, 13065},\n",
       "             1983: {1896, 5607, 7190, 8190, 10561, 12590, 13356},\n",
       "             2690: {5501, 7071, 10100, 10179, 10671, 11108, 11403},\n",
       "             3022: {800, 2578, 4929, 5137, 9122, 12113},\n",
       "             2483: {874, 3446, 4674, 6044, 7241, 10173},\n",
       "             1471: {1879, 3714, 8375, 12819, 13110, 13118},\n",
       "             1298: {1896, 4448, 8190, 9808, 10434, 10451, 10482},\n",
       "             2631: {1159, 2958, 5031, 7533, 7951, 9907},\n",
       "             3339: {2660, 3446, 4000, 4674, 8779, 10173},\n",
       "             78: {422, 3386, 4387, 7190, 8064, 11251},\n",
       "             939: {1234, 1365, 1803, 1896, 6452, 8190, 9482, 11960},\n",
       "             123: {1715, 3107, 4444, 4674, 8779, 10173},\n",
       "             2994: {842, 2039, 8105, 8942, 9228, 10799},\n",
       "             695: {1260, 7813, 8073, 8529, 9280, 9370, 9620},\n",
       "             0: {470, 1560, 2766, 5073, 8954},\n",
       "             1679: {3095, 3605, 4347, 7391, 7885, 8908, 8931, 9373, 11928},\n",
       "             2445: {145, 594, 1055, 3775, 7389},\n",
       "             1710: {4560, 7257, 8984, 10935, 11749, 12370},\n",
       "             3062: {1896, 3334, 4448, 8190, 10500, 12532},\n",
       "             247: {1807,\n",
       "              1887,\n",
       "              6095,\n",
       "              7606,\n",
       "              10116,\n",
       "              10146,\n",
       "              11232,\n",
       "              12905,\n",
       "              13005,\n",
       "              13316},\n",
       "             57: {430, 3002, 5118, 5629, 9002, 10429, 10485},\n",
       "             3385: {594, 3893, 7929, 9102, 10364, 13115},\n",
       "             2987: {2104,\n",
       "              2515,\n",
       "              2923,\n",
       "              3052,\n",
       "              4259,\n",
       "              5938,\n",
       "              5981,\n",
       "              6410,\n",
       "              6780,\n",
       "              8656,\n",
       "              9291,\n",
       "              9300,\n",
       "              9461,\n",
       "              9568,\n",
       "              9627,\n",
       "              9634,\n",
       "              10167,\n",
       "              10530,\n",
       "              10747,\n",
       "              11043,\n",
       "              11378,\n",
       "              12550,\n",
       "              13035},\n",
       "             3099: {2, 1544, 1730, 2311, 10004, 11481, 11752},\n",
       "             1396: {7939, 9036, 9174, 10196, 10739, 12015},\n",
       "             3167: {4249, 6073, 6991, 7359, 10786, 12339},\n",
       "             1466: {4137, 5284, 6201, 6282, 9549, 12615},\n",
       "             179: {3564, 4123, 5125, 5761, 10822, 13229},\n",
       "             1623: {960, 2074, 3138, 5672, 6009, 11923},\n",
       "             2349: {1254, 2000, 2452, 4876, 6092, 13138},\n",
       "             1760: {127, 5632, 8600, 9285, 9414, 11985, 12140},\n",
       "             2235: {2729, 4967, 6318, 7071, 8744, 11403, 11673, 12330, 13350},\n",
       "             3034: {440, 5944, 7107, 10038, 12330},\n",
       "             2940: {378, 714, 957, 8223, 9616, 13291},\n",
       "             662: {802, 4312, 5501, 8200, 10724},\n",
       "             416: {2437, 4995, 10118, 10355, 11009, 12162},\n",
       "             2710: {646, 5461, 6468, 6477, 8831, 12012},\n",
       "             1570: {957, 1022, 2358, 5208, 7176, 8223, 12400},\n",
       "             1086: {1123, 1521, 1896, 3638, 5452, 12868},\n",
       "             2674: {56, 3251, 3587, 8190, 8605, 12782},\n",
       "             1757: {4407, 5371, 7800, 7888, 8828, 12007},\n",
       "             1262: {3107, 3446, 4000, 4674, 6044, 10173},\n",
       "             655: {119, 2681, 9873, 9912, 10055, 13115},\n",
       "             769: {276, 2964, 4605, 5944, 10001},\n",
       "             2859: {1234, 1896, 3871, 5318, 5607, 8190},\n",
       "             2872: {1728, 2397, 4136, 7887, 10351},\n",
       "             2887: {1151, 7224, 11070, 11296, 11946, 13219},\n",
       "             1123: {751, 868, 2139, 5398, 5631, 6989},\n",
       "             1597: {217,\n",
       "              1388,\n",
       "              1752,\n",
       "              1753,\n",
       "              2516,\n",
       "              3171,\n",
       "              3908,\n",
       "              4575,\n",
       "              5051,\n",
       "              5388,\n",
       "              6340,\n",
       "              7464,\n",
       "              8302,\n",
       "              8669,\n",
       "              9340,\n",
       "              9633,\n",
       "              9829,\n",
       "              11057,\n",
       "              11996,\n",
       "              12452,\n",
       "              12690,\n",
       "              12732},\n",
       "             730: {874, 4674, 6044, 7241, 8779, 10173},\n",
       "             69: {647, 4713, 7270, 9723, 13042, 13245},\n",
       "             2480: {1132,\n",
       "              1189,\n",
       "              1661,\n",
       "              2452,\n",
       "              3985,\n",
       "              4588,\n",
       "              4876,\n",
       "              6557,\n",
       "              8359,\n",
       "              9923,\n",
       "              11494,\n",
       "              12671},\n",
       "             256: {1541, 2949, 3090, 5144, 9809, 11293},\n",
       "             735: {1285, 3503, 5414, 5461, 10437, 10870, 13019},\n",
       "             2375: {2920, 4075, 8263, 10000, 10984, 12806},\n",
       "             1795: {132, 874, 3107, 4674, 7154, 9125},\n",
       "             1311: {3157,\n",
       "              4000,\n",
       "              4599,\n",
       "              5438,\n",
       "              7039,\n",
       "              7353,\n",
       "              8501,\n",
       "              10169,\n",
       "              11389,\n",
       "              13274},\n",
       "             1571: {2569, 6794, 7146, 7549, 12484, 12699},\n",
       "             1087: {1157, 3996, 4045, 10658, 10949, 12005},\n",
       "             1940: {746, 1896, 3093, 4448, 8190, 9313, 10434, 10500},\n",
       "             2439: {5094, 5468, 8852, 9463, 11312, 12361},\n",
       "             3120: {3107, 3446, 4000, 4674, 9125, 13274},\n",
       "             3074: {1011, 1371, 6630, 8711, 9439, 10503},\n",
       "             2322: {1896, 2578, 4448, 8190, 10434, 10500},\n",
       "             967: {1020, 4793, 7215, 8345, 11569, 12786},\n",
       "             1185: {591, 2498, 3957, 8190, 9059},\n",
       "             1357: {412,\n",
       "              3228,\n",
       "              3407,\n",
       "              4312,\n",
       "              4407,\n",
       "              4790,\n",
       "              5419,\n",
       "              5586,\n",
       "              5945,\n",
       "              8200,\n",
       "              8223,\n",
       "              8831,\n",
       "              9009,\n",
       "              9386,\n",
       "              9870,\n",
       "              10930,\n",
       "              12187,\n",
       "              12490},\n",
       "             3236: {4811, 6141, 6424, 6756, 7000},\n",
       "             3190: {6405, 7130, 7724, 8329, 8498, 11255},\n",
       "             2316: {967, 2863, 5437, 7577, 11752, 12004},\n",
       "             2882: {1217, 2884, 4407, 9580, 12485, 12744},\n",
       "             118: {2627, 4203, 4699, 7028, 11611, 12236},\n",
       "             116: {3647, 5624, 9010, 9031, 12646},\n",
       "             1825: {1896, 3656, 5501, 7190, 9674, 11214, 11713},\n",
       "             1057: {2662, 3512, 4988, 8964, 9936, 10938},\n",
       "             1584: {3759,\n",
       "              4467,\n",
       "              4524,\n",
       "              5262,\n",
       "              5280,\n",
       "              6040,\n",
       "              6421,\n",
       "              7234,\n",
       "              7709,\n",
       "              8205,\n",
       "              8371,\n",
       "              8833,\n",
       "              9886,\n",
       "              11013,\n",
       "              11192,\n",
       "              11529,\n",
       "              12015,\n",
       "              12910},\n",
       "             462: {1383, 1896, 7190, 8190, 8777, 12071},\n",
       "             2795: {1126, 2571, 4392, 5220, 5586, 6468, 8200, 12230},\n",
       "             3262: {1896, 3342, 4448, 8190, 10434, 10500},\n",
       "             1092: {5718, 7318, 7849, 8601, 9405, 10267, 12475},\n",
       "             2155: {1217, 6543, 9251, 9959, 9970, 11460},\n",
       "             528: {5465, 5586, 5905, 6187, 8402, 9009},\n",
       "             1715: {1115,\n",
       "              3323,\n",
       "              6208,\n",
       "              6293,\n",
       "              7671,\n",
       "              9219,\n",
       "              9626,\n",
       "              10324,\n",
       "              12668,\n",
       "              13200},\n",
       "             2695: {224, 3446, 4000, 4674, 10173},\n",
       "             326: {3107, 3157, 4674, 8779, 9125, 10173},\n",
       "             1568: {2102, 3038, 5178, 6140, 6248, 6501, 9067, 10773},\n",
       "             2668: {580, 962, 7711, 9010, 10234, 11752, 12646},\n",
       "             368: {2218, 3839, 6805, 10152, 12267, 12278},\n",
       "             2790: {1896, 3334, 8190, 8935, 10539, 12972},\n",
       "             588: {3617, 8760, 10591, 12636, 12868},\n",
       "             1908: {531, 2961, 4246, 6650, 8046, 8610},\n",
       "             1796: {5822, 7580, 9254, 11377, 12110},\n",
       "             355: {975, 1896, 4448, 8190, 10434, 10500, 11747},\n",
       "             1249: {124, 4868, 7292, 9698, 10359, 11731, 11809, 12966},\n",
       "             1247: {1792, 9011, 9413, 11361, 11919, 13006},\n",
       "             849: {1863, 2287, 4277, 7650, 7675, 8779},\n",
       "             313: {5094, 7378, 7687, 9080, 9463},\n",
       "             2231: {1896, 3144, 3871, 5546, 5607, 8190, 8299, 9761, 12330},\n",
       "             2774: {1037, 1105, 3051, 11212, 12464, 12689},\n",
       "             2588: {1896, 3515, 4448, 7877, 8190, 10434},\n",
       "             2896: {1896, 4448, 4630, 7190, 8190, 10434, 10451, 12500},\n",
       "             1251: {4448, 4859, 8190, 10434, 11170, 12586},\n",
       "             1031: {589, 1447, 3623, 8082, 11439, 12600},\n",
       "             120: {1287, 3692, 4808, 8328, 8889, 12065},\n",
       "             1124: {1164, 4848, 6434, 7711, 8307, 11752, 12240, 12313, 12917},\n",
       "             1851: {1929, 2123, 4194, 5262, 7834, 8098},\n",
       "             287: {849, 1126, 1993, 8402, 12590, 12593},\n",
       "             816: {2852, 3070, 3075, 5501, 9171, 11594, 13212},\n",
       "             1809: {1371, 5270, 6630, 7704, 9439},\n",
       "             2655: {464,\n",
       "              680,\n",
       "              2964,\n",
       "              3407,\n",
       "              4991,\n",
       "              7127,\n",
       "              7542,\n",
       "              8070,\n",
       "              8992,\n",
       "              10802,\n",
       "              12451},\n",
       "             1986: {1315, 1724, 4499, 4660, 4940, 4992, 5372, 11762},\n",
       "             1844: {1455, 2762, 4223, 4802, 7928, 10383, 11755},\n",
       "             2152: {1896, 3489, 7190, 8190, 9847, 12041},\n",
       "             2841: {246, 6731, 10884, 10954},\n",
       "             1859: {2706, 6212, 7090, 7161, 11858, 12042},\n",
       "             2302: {3572, 5760, 7735, 10550, 11983, 12210, 12992},\n",
       "             1049: {895, 5010, 5869, 6297, 6950, 10384},\n",
       "             2575: {990, 1722, 3576, 10535, 11325, 11533},\n",
       "             1567: {4614, 5311, 7593, 9481, 10385, 11184},\n",
       "             2221: {4857, 7149, 9131, 9511, 10080, 12625},\n",
       "             370: {87, 1663, 2788, 6555, 8162, 10610, 11441},\n",
       "             1752: {2924,\n",
       "              3262,\n",
       "              4683,\n",
       "              4979,\n",
       "              5853,\n",
       "              6107,\n",
       "              8155,\n",
       "              9788,\n",
       "              10862,\n",
       "              12094,\n",
       "              12152,\n",
       "              12532,\n",
       "              13224},\n",
       "             1593: {2857, 6365, 7345, 10782},\n",
       "             474: {1113, 2174, 4674, 4811, 6141, 7951},\n",
       "             2255: {2841,\n",
       "              3238,\n",
       "              3757,\n",
       "              4094,\n",
       "              7483,\n",
       "              7665,\n",
       "              10647,\n",
       "              11423,\n",
       "              12197,\n",
       "              12810,\n",
       "              13198,\n",
       "              13372},\n",
       "             2918: {953, 3039, 3871, 7622, 8190, 11701, 12590},\n",
       "             2241: {4049, 6050, 6525, 8230, 11059, 12306},\n",
       "             1324: {1146,\n",
       "              1210,\n",
       "              1578,\n",
       "              2446,\n",
       "              3290,\n",
       "              3482,\n",
       "              4397,\n",
       "              6855,\n",
       "              8378,\n",
       "              9753,\n",
       "              11006,\n",
       "              11896,\n",
       "              12151,\n",
       "              12253},\n",
       "             761: {1978, 4383, 10217, 12136, 12660, 12900},\n",
       "             2570: {1483, 4989, 5308, 5612, 11873, 13055},\n",
       "             3053: {362, 4475, 6036, 6406, 11116, 12650},\n",
       "             3307: {1656, 1896, 2856, 3091, 4389, 5546, 10512},\n",
       "             2441: {114,\n",
       "              405,\n",
       "              1314,\n",
       "              1518,\n",
       "              1936,\n",
       "              2317,\n",
       "              3263,\n",
       "              4142,\n",
       "              5901,\n",
       "              5991,\n",
       "              6013,\n",
       "              6668,\n",
       "              10603,\n",
       "              12495,\n",
       "              12758},\n",
       "             1723: {2666, 2926, 5080, 5642, 6276, 7418, 9498, 9667, 12297},\n",
       "             1936: {719, 2860, 7841, 9573, 9837, 12410},\n",
       "             2260: {795, 3004, 6287, 7819, 7888, 12239, 12354},\n",
       "             733: {802, 1583, 5220, 6967, 10001, 10247, 11594},\n",
       "             1981: {3327, 6890, 8848, 8873, 9916, 11643, 11812},\n",
       "             2518: {942, 8620, 9072, 9754, 10913, 13283},\n",
       "             2146: {263, 4297, 4584, 8285, 8711, 10413, 11121, 11584},\n",
       "             1642: {2946, 6915, 8261, 10091, 11696, 12410},\n",
       "             558: {1383, 1896, 4448, 8190, 8297, 10434, 10500},\n",
       "             197: {600, 1096, 2205, 3607, 7050, 7570, 9867, 12401},\n",
       "             196: {3039, 5798, 10443, 12590},\n",
       "             140: {427, 1021, 3039, 7677, 8200, 10092, 12491, 12593},\n",
       "             3135: {1993, 2206, 4312, 5414, 8200, 10929},\n",
       "             2760: {440, 5335, 5546, 7842, 8021, 8116},\n",
       "             2143: {2266, 5797, 6044, 7026, 7977, 9472},\n",
       "             2968: {4217, 7852, 12156, 12710},\n",
       "             931: {1868, 6582, 6707, 6825, 7409, 7888},\n",
       "             2903: {330, 2403, 2517, 5721, 7145, 9887, 11546, 11944},\n",
       "             1839: {224,\n",
       "              2660,\n",
       "              3107,\n",
       "              3446,\n",
       "              4000,\n",
       "              4674,\n",
       "              7241,\n",
       "              8779,\n",
       "              9125,\n",
       "              10173,\n",
       "              12869},\n",
       "             2817: {1523, 3903, 5515, 7768, 9036, 12936},\n",
       "             1862: {1896, 3334, 5972, 7190, 8190, 10434, 11563, 12500},\n",
       "             1783: {2247, 3551, 5094, 7687, 8695, 12832},\n",
       "             361: {4054, 4901, 6044, 7675, 8779, 10034},\n",
       "             2309: {4448, 8190, 9313, 9479, 10500, 11064},\n",
       "             1138: {6967, 8225, 9006, 9870, 11055, 12187},\n",
       "             2115: {1367, 2459, 4086, 9515, 10819, 11010, 11038, 12784, 12909},\n",
       "             1813: {3588,\n",
       "              5439,\n",
       "              6547,\n",
       "              10551,\n",
       "              11370,\n",
       "              11644,\n",
       "              12743,\n",
       "              13256,\n",
       "              13325},\n",
       "             747: {1812,\n",
       "              2189,\n",
       "              3255,\n",
       "              3503,\n",
       "              4427,\n",
       "              5572,\n",
       "              6286,\n",
       "              7888,\n",
       "              8364,\n",
       "              8795,\n",
       "              9384,\n",
       "              9741,\n",
       "              9767,\n",
       "              10038,\n",
       "              11898,\n",
       "              12463,\n",
       "              12593},\n",
       "             3373: {88, 736, 1019, 1035, 8819, 11785, 13282},\n",
       "             1972: {3511, 5048, 5189, 10027, 10630, 13410},\n",
       "             2238: {671,\n",
       "              2443,\n",
       "              2875,\n",
       "              2944,\n",
       "              3042,\n",
       "              3043,\n",
       "              3500,\n",
       "              4329,\n",
       "              4365,\n",
       "              5516,\n",
       "              5714,\n",
       "              7626,\n",
       "              7769,\n",
       "              8945,\n",
       "              9499,\n",
       "              11674,\n",
       "              12888},\n",
       "             1412: {4122, 4817, 7123, 11335, 11793, 13141},\n",
       "             684: {431, 1740, 6699, 7956, 11505, 12757, 13191},\n",
       "             2458: {241,\n",
       "              1981,\n",
       "              2027,\n",
       "              2545,\n",
       "              3393,\n",
       "              6432,\n",
       "              6524,\n",
       "              9147,\n",
       "              12375,\n",
       "              12449},\n",
       "             946: {1481,\n",
       "              1595,\n",
       "              1678,\n",
       "              3517,\n",
       "              4969,\n",
       "              5522,\n",
       "              5899,\n",
       "              6722,\n",
       "              7452,\n",
       "              9043,\n",
       "              10817,\n",
       "              10989,\n",
       "              11352},\n",
       "             3219: {302, 5434, 5512, 7762, 9559, 9737},\n",
       "             1252: {615, 2242, 4878, 7440, 8632, 10751, 12976},\n",
       "             2798: {1371, 6630, 7419, 7946, 8711, 9096, 9439, 11584},\n",
       "             845: {443, 1605, 3631, 3894, 4823, 6625},\n",
       "             745: {2012, 4746, 9065, 9958, 10805, 12146},\n",
       "             59: {679,\n",
       "              1896,\n",
       "              3039,\n",
       "              4967,\n",
       "              6318,\n",
       "              7071,\n",
       "              8190,\n",
       "              9171,\n",
       "              10179,\n",
       "              11403,\n",
       "              13212},\n",
       "             2515: {4084, 5423, 10477, 12365},\n",
       "             2298: {802, 958, 2981, 4646, 5762, 12846},\n",
       "             532: {224, 4444, 4674, 6044, 8779, 10173},\n",
       "             995: {1477, 1758, 2806, 4752, 9966, 12153},\n",
       "             1105: {703, 1308, 6097, 6953, 9349, 9453},\n",
       "             2654: {1222, 3446, 4000, 4674, 8779, 10173, 12498},\n",
       "             647: {132, 2660, 4000, 4444, 4674, 10173},\n",
       "             2369: {9081, 9173, 11176, 12131, 12183, 12468},\n",
       "             2166: {969, 2578, 3335, 4141, 7653, 13150},\n",
       "             1234: {1383, 4366, 4433, 5874, 12591, 12757, 12779},\n",
       "             164: {3933, 5433, 5595, 6385, 11368, 12591, 12757, 12993},\n",
       "             1136: {1896, 2367, 5546, 5830, 10279, 11214},\n",
       "             1992: {1923, 1958, 6267, 9531, 10929, 11594, 12103},\n",
       "             1350: {2971, 3096, 4412, 5275, 6530, 12499},\n",
       "             2526: {3446, 4674, 7241, 7353, 8779, 10173, 12476},\n",
       "             1610: {1851, 2060, 7077, 8996, 10858, 13186},\n",
       "             1553: {431, 1383, 1386, 3334, 11767, 12384, 12757},\n",
       "             1048: {3017,\n",
       "              3071,\n",
       "              4222,\n",
       "              5267,\n",
       "              8170,\n",
       "              9240,\n",
       "              9726,\n",
       "              10524,\n",
       "              11530,\n",
       "              12147,\n",
       "              12329,\n",
       "              13126},\n",
       "             628: {317, 6745, 9244, 10291, 12175, 12660},\n",
       "             2486: {1800, 4217, 9912, 11432, 12591, 12757},\n",
       "             1418: {533, 585, 2308, 4044, 9833, 10280},\n",
       "             2366: {2518, 2737, 5613, 7962, 8249, 9404},\n",
       "             2519: {3051, 3228, 4407, 6468, 8787, 11882},\n",
       "             1325: {1383, 1896, 4697, 5412, 8190, 9628, 10552},\n",
       "             1563: {143,\n",
       "              1383,\n",
       "              1698,\n",
       "              1896,\n",
       "              5429,\n",
       "              6273,\n",
       "              7190,\n",
       "              7404,\n",
       "              8190,\n",
       "              12785},\n",
       "             1046: {1223, 2158, 4870, 7615, 11129, 11313},\n",
       "             2168: {53, 1259, 1476, 1563, 5706, 7377, 11689, 13276, 13385},\n",
       "             1468: {1496, 4307, 6447, 8396, 10109, 11145},\n",
       "             3346: {2727, 5313, 6127, 8441, 9416, 10004, 11752},\n",
       "             3159: {51,\n",
       "              1652,\n",
       "              2989,\n",
       "              3135,\n",
       "              3213,\n",
       "              4385,\n",
       "              5077,\n",
       "              5483,\n",
       "              5924,\n",
       "              11248,\n",
       "              13341},\n",
       "             765: {2038, 3144, 4312, 4553, 10409, 12239},\n",
       "             2704: {348, 1353, 5840, 6798, 8674, 13052},\n",
       "             17: {378, 2358, 4089, 4942, 5953, 6713, 10351, 12400},\n",
       "             2532: {1371, 6945, 7287, 7419, 8711, 11584},\n",
       "             3184: {211, 1995, 4102, 4667, 5088, 7889},\n",
       "             2367: {460, 4830, 7814, 8641, 9485, 10698},\n",
       "             2428: {82,\n",
       "              549,\n",
       "              1264,\n",
       "              2281,\n",
       "              2385,\n",
       "              2731,\n",
       "              3953,\n",
       "              4164,\n",
       "              5774,\n",
       "              5867,\n",
       "              6407,\n",
       "              7165,\n",
       "              7674,\n",
       "              7806,\n",
       "              8124,\n",
       "              9276,\n",
       "              9521,\n",
       "              9584,\n",
       "              10203,\n",
       "              10229,\n",
       "              11341,\n",
       "              13026},\n",
       "             75: {4820, 5037, 5979, 8680, 10648, 10669},\n",
       "             3355: {260, 1057, 5389, 6364, 6592, 8555, 10038, 10504, 13119},\n",
       "             545: {1648, 4597, 6147, 7525, 7754, 9422},\n",
       "             2520: {761, 3386, 5804, 6452, 8462, 11960},\n",
       "             2093: {368, 1291, 3304, 3435, 7405, 11244, 12782, 12889},\n",
       "             1214: {743, 1874, 4950, 5381, 5635, 9908, 10623, 10937},\n",
       "             1194: {1593, 1602, 8743, 9298, 12747, 13342},\n",
       "             980: {1113, 2003, 6424, 6756, 7951, 11954},\n",
       "             1863: {4398, 7401, 7575, 10844, 11128},\n",
       "             1677: {3137, 6921, 9462, 9993, 10818, 12321},\n",
       "             2622: {1896, 4448, 7190, 8190, 10434, 10500},\n",
       "             189: {5018, 6060, 8962, 10086},\n",
       "             799: {2231, 4250, 5249, 5559, 6935, 8063, 9596},\n",
       "             1301: {1896, 3871, 4967, 5607, 6318, 6468, 7071, 8190, 11403},\n",
       "             3006: {2337, 3068, 5935, 7705, 11661, 12348},\n",
       "             2212: {389, 850, 4094, 4556, 5179, 5202, 5390, 10292},\n",
       "             3205: {377, 2660, 3107, 4674, 7353, 9125},\n",
       "             2105: {1341, 2631, 5094, 5468, 6074, 8852, 9463},\n",
       "             1604: {2084, 2499, 4537, 6163, 7446, 8252, 9447},\n",
       "             2787: {1855, 4756, 6456, 11373, 11927, 12606},\n",
       "             1240: {500,\n",
       "              1130,\n",
       "              1896,\n",
       "              3334,\n",
       "              4448,\n",
       "              7190,\n",
       "              8190,\n",
       "              10434,\n",
       "              10713,\n",
       "              10987},\n",
       "             836: {8021, 8122, 8215, 11594, 12241, 12292},\n",
       "             636: {1769,\n",
       "              2290,\n",
       "              3815,\n",
       "              4930,\n",
       "              5123,\n",
       "              5758,\n",
       "              7413,\n",
       "              7994,\n",
       "              8662,\n",
       "              8998,\n",
       "              10398,\n",
       "              11851,\n",
       "              12560,\n",
       "              12766,\n",
       "              12874},\n",
       "             2175: {285, 2602, 4285, 4297, 5113, 5535, 9569},\n",
       "             531: {1896, 4448, 7190, 8190, 10434, 12500},\n",
       "             364: {1113, 4674, 5063, 6756, 7951, 11954},\n",
       "             3128: {132, 3107, 4000, 4674, 9125, 13274},\n",
       "             27: {377,\n",
       "              1222,\n",
       "              2287,\n",
       "              4674,\n",
       "              5346,\n",
       "              6044,\n",
       "              7241,\n",
       "              7434,\n",
       "              7650,\n",
       "              9446,\n",
       "              9904,\n",
       "              10173},\n",
       "             1520: {378, 1583, 5944, 9761, 10351, 12820},\n",
       "             1892: {3407, 4407, 8519, 11802, 12012, 12571},\n",
       "             2823: {989, 1900, 1975, 4887, 11032, 12196},\n",
       "             1864: {4902, 5060, 6192, 9166, 12657, 12989},\n",
       "             2088: {2010, 2647, 4993, 5450, 7942, 8333, 11253},\n",
       "             1728: {2143, 2932, 5848, 6711, 6887, 9123, 10508, 10642, 11424},\n",
       "             2440: {3514, 6122, 8044, 8305, 9155, 11577, 11607, 12825},\n",
       "             437: {3829, 7254, 8949, 9416, 10234, 11752},\n",
       "             266: {7632, 9878, 10576, 10969, 11285, 11678},\n",
       "             2233: {4448, 10500, 12277, 12790},\n",
       "             1848: {2043, 5161, 7991, 8702, 9280, 9370},\n",
       "             1008: {779, 1896, 7190, 7771, 9256, 13342},\n",
       "             2821: {186, 1371, 2602, 2991, 4297, 8711, 9096},\n",
       "             234: {4104, 7232, 8827, 8832, 11531, 12058},\n",
       "             449: {3334, 3857, 4448, 8190, 9913, 12294},\n",
       "             2767: {1609, 2470, 3881, 4369, 4654, 5810, 8366},\n",
       "             3162: {132, 3107, 3937, 4000, 4227, 7353},\n",
       "             1400: {322, 668, 6699, 7058, 9435, 10571, 10854},\n",
       "             285: {217, 5490, 5508, 8587, 9579, 9878},\n",
       "             1691: {1275, 3005, 4399, 5779, 6021, 6597, 8665, 11436},\n",
       "             262: {2512, 5031, 6756, 7533, 7951, 9907},\n",
       "             754: {1362, 1896, 3040, 3656, 5546, 7190, 7194, 9863, 11214},\n",
       "             1446: {2038, 3822, 4790, 5414, 6468},\n",
       "             1991: {2908, 4439, 6044, 9440, 10173, 12303},\n",
       "             699: {1896, 3128, 3871, 5607, 7622, 7924, 8190, 10765, 12590},\n",
       "             1674: {3830, 5286, 8355, 9384, 11275, 13040},\n",
       "             2151: {377, 2660, 3446, 4674, 8779, 9125, 10173},\n",
       "             688: {2351, 3040, 5145, 6318, 7071, 10671, 11403, 13356},\n",
       "             2107: {440, 1338, 3411, 5563, 8660, 9076, 9216, 10342},\n",
       "             594: {200, 3335, 6408, 6744, 8502, 9060},\n",
       "             315: {2782,\n",
       "              4694,\n",
       "              7598,\n",
       "              7603,\n",
       "              7861,\n",
       "              8463,\n",
       "              8625,\n",
       "              8694,\n",
       "              9947,\n",
       "              9995,\n",
       "              10051,\n",
       "              12420},\n",
       "             569: {1323, 5733, 5784, 6627, 6828, 9151, 10958, 11114},\n",
       "             177: {1656, 3039, 3480, 4722, 9745, 11959},\n",
       "             1380: {1456, 3965, 4157, 4389, 6317, 6636, 10038},\n",
       "             2666: {6903, 7068, 7627, 8772, 10262, 10969},\n",
       "             3281: {722, 795, 1242, 4933, 7307, 9204},\n",
       "             2592: {3107, 4444, 4674, 6044, 9125, 10173, 12869},\n",
       "             953: {1997, 2191, 4510, 6840, 9326, 10175, 11547, 12416},\n",
       "             2065: {3760, 5831, 7845, 7855, 11468, 12268, 12311},\n",
       "             2842: {1817,\n",
       "              4984,\n",
       "              5047,\n",
       "              5478,\n",
       "              6097,\n",
       "              6840,\n",
       "              8077,\n",
       "              8212,\n",
       "              10267,\n",
       "              11063,\n",
       "              11651,\n",
       "              11873},\n",
       "             1526: {583, 1896, 2654, 4452, 5318, 6238, 6298, 7190, 7594, 8190},\n",
       "             460: {1285, 6399, 8200, 12239, 12354, 12765},\n",
       "             3114: {1896, 2578, 2882, 3334, 4448, 5959, 6291, 8190, 10434},\n",
       "             2898: {341, 2034, 6546, 10564, 12501},\n",
       "             2079: {5010, 5048, 5869, 8938, 9444, 11151},\n",
       "             1631: {3172, 7249, 7835, 8707, 10987, 11064},\n",
       "             1707: {558,\n",
       "              2246,\n",
       "              3773,\n",
       "              3885,\n",
       "              5304,\n",
       "              5968,\n",
       "              7017,\n",
       "              7919,\n",
       "              8815,\n",
       "              9399,\n",
       "              9427,\n",
       "              9520,\n",
       "              10663,\n",
       "              11332,\n",
       "              11474,\n",
       "              12619},\n",
       "             2844: {2660, 3446, 4674, 7241, 8779, 10173},\n",
       "             482: {1222, 3107, 4674, 8281, 9125, 10173},\n",
       "             1680: {655, 2695, 2866, 4032, 5431, 6975, 9119},\n",
       "             2884: {132, 2660, 3446, 4674, 8779, 10173},\n",
       "             142: {422, 1896, 2588, 3386, 3572, 8190},\n",
       "             125: {377, 874, 2660, 3107, 4000, 4674, 8779, 9125, 10173, 12869},\n",
       "             356: {3049, 5277, 5675, 6356, 10211, 12009},\n",
       "             1068: {132, 4227, 4674, 6044, 9125, 13274},\n",
       "             1629: {1896, 3386, 4106, 7190, 8190, 11758},\n",
       "             1109: {2660, 3107, 4444, 4674, 8779, 9125},\n",
       "             2337: {1026, 3122, 3598, 7723, 9337, 12773},\n",
       "             3044: {3489, 6617, 7190, 8922, 9813},\n",
       "             1492: {5205, 6054, 8766, 10473, 11383, 11613, 12593},\n",
       "             2392: {231, 507, 727, 1009, 11438},\n",
       "             2816: {77, 3060, 4146, 5064, 8200, 9061, 12201, 13075},\n",
       "             1130: {1095, 5234, 5501, 7059, 9217, 10499},\n",
       "             1356: {2389, 2501, 6056, 6103, 7930, 9851},\n",
       "             1151: {400,\n",
       "              848,\n",
       "              915,\n",
       "              994,\n",
       "              1746,\n",
       "              2186,\n",
       "              2301,\n",
       "              2407,\n",
       "              2478,\n",
       "              2589,\n",
       "              3669,\n",
       "              3729,\n",
       "              3740,\n",
       "              4029,\n",
       "              4284,\n",
       "              4431,\n",
       "              4874,\n",
       "              5377,\n",
       "              5640,\n",
       "              6059,\n",
       "              6659,\n",
       "              6831,\n",
       "              6889,\n",
       "              7174,\n",
       "              7490,\n",
       "              7515,\n",
       "              7605,\n",
       "              7936,\n",
       "              8306,\n",
       "              8546,\n",
       "              8671,\n",
       "              8768,\n",
       "              9224,\n",
       "              9563,\n",
       "              10258,\n",
       "              10306,\n",
       "              10454,\n",
       "              10525,\n",
       "              10641,\n",
       "              11167,\n",
       "              11587,\n",
       "              11624,\n",
       "              11721,\n",
       "              11765,\n",
       "              12551,\n",
       "              12681,\n",
       "              12683,\n",
       "              13230,\n",
       "              13279},\n",
       "             1735: {186, 1371, 2100, 4293, 5270, 11584},\n",
       "             1950: {4018, 7879, 8023, 8408, 8772, 10856, 11357},\n",
       "             2847: {5710, 7389, 7513, 9497, 11764, 12528},\n",
       "             2465: {1371, 3436, 4293, 5270, 7287, 10024},\n",
       "             1773: {56, 1239, 1896, 8190, 9724, 11090},\n",
       "             3302: {529, 871, 1489, 2901, 3123, 6066},\n",
       "             721: {155,\n",
       "              397,\n",
       "              723,\n",
       "              747,\n",
       "              1327,\n",
       "              2146,\n",
       "              2741,\n",
       "              3388,\n",
       "              3437,\n",
       "              4463,\n",
       "              5235,\n",
       "              5832,\n",
       "              5966,\n",
       "              6472,\n",
       "              6776,\n",
       "              6928,\n",
       "              8308,\n",
       "              8963,\n",
       "              10075,\n",
       "              10502,\n",
       "              10742,\n",
       "              11900,\n",
       "              12243,\n",
       "              12246,\n",
       "              12383,\n",
       "              13001,\n",
       "              13380},\n",
       "             2156: {4398, 5140, 5199, 5669, 7014, 8587},\n",
       "             554: {388, 5681, 7744, 9130, 10338, 11599, 11752},\n",
       "             1431: {206, 3062, 3945, 4460, 5624, 6117, 12308},\n",
       "             899: {524,\n",
       "              4339,\n",
       "              5015,\n",
       "              5301,\n",
       "              7628,\n",
       "              8467,\n",
       "              9716,\n",
       "              10457,\n",
       "              10772,\n",
       "              11091},\n",
       "             434: {1136, 2439, 2544, 2617, 8165, 9317, 9832, 10752, 12840},\n",
       "             270: {1104, 1404, 1826, 3270, 4216, 6262, 11050, 13173},\n",
       "             3287: {927, 1039, 2745, 2787, 4241, 12410},\n",
       "             2810: {1383, 2432, 2578, 10097, 10500, 10529},\n",
       "             591: {5446, 6478, 7857, 8448, 11288, 12753},\n",
       "             466: {1896, 3604, 7190, 10434, 10500, 11564, 13069},\n",
       "             2653: {1655, 3222, 4333, 4623, 5331, 12176},\n",
       "             63: {957, 1583, 5945, 6713, 6967, 12187},\n",
       "             1877: {2620, 2837, 7363, 8445, 8999, 10484},\n",
       "             871: {557, 752, 912, 2447, 4006, 6818, 9749, 9787},\n",
       "             2692: {937, 5592, 6768, 12071, 12170, 12757},\n",
       "             295: {2772, 3207, 7451, 9574, 9710},\n",
       "             1560: {911,\n",
       "              1239,\n",
       "              1383,\n",
       "              1434,\n",
       "              2431,\n",
       "              6119,\n",
       "              6232,\n",
       "              7653,\n",
       "              9913,\n",
       "              12122},\n",
       "             2491: {4034, 6545, 8290, 9587, 12001},\n",
       "             99: {2460, 2980, 11217, 12454, 13066, 13233},\n",
       "             1499: {311, 2017, 4750, 4996, 6919, 10224},\n",
       "             2246: {2036,\n",
       "              2258,\n",
       "              2998,\n",
       "              4286,\n",
       "              5172,\n",
       "              5460,\n",
       "              5707,\n",
       "              8047,\n",
       "              8640,\n",
       "              11845,\n",
       "              12925,\n",
       "              12944},\n",
       "             2033: {5288,\n",
       "              6189,\n",
       "              6306,\n",
       "              7379,\n",
       "              10104,\n",
       "              10667,\n",
       "              10759,\n",
       "              10924,\n",
       "              11420,\n",
       "              13411},\n",
       "             1517: {1062, 3822, 5115, 5461, 9863, 10829},\n",
       "             2163: {178,\n",
       "              270,\n",
       "              788,\n",
       "              3863,\n",
       "              4224,\n",
       "              4288,\n",
       "              5252,\n",
       "              5764,\n",
       "              5782,\n",
       "              6319,\n",
       "              6587,\n",
       "              7070,\n",
       "              7274,\n",
       "              9134,\n",
       "              9748,\n",
       "              10632,\n",
       "              11069,\n",
       "              11333,\n",
       "              12557},\n",
       "             3226: {835, 2028, 10335, 11421, 11667, 11787},\n",
       "             2682: {1675, 1896, 3334, 4448, 8190, 10434},\n",
       "             2396: {377, 3157, 4444, 4674, 6044, 8779, 10173},\n",
       "             184: {2602, 4297, 5558, 6181, 7287, 11345},\n",
       "             3199: {344, 538, 957, 4707, 5208, 8071, 8223, 10202},\n",
       "             2986: {377, 3908, 9064, 9978},\n",
       "             2948: {4967, 7071, 7840, 11403, 11479, 11542},\n",
       "             2314: {651, 7254, 7268, 7285, 10234, 11752},\n",
       "             2061: {132, 3446, 4000, 4674, 7353, 8779, 10173},\n",
       "             2283: {2361, 3202, 5448, 8260, 9633, 11638, 12452},\n",
       "             2851: {2305, 6938, 8091, 8763, 9435, 11653},\n",
       "             611: {757, 1239, 4517, 7494, 7560},\n",
       "             2391: {1583, 4017, 5944, 7887, 8035, 12354},\n",
       "             1790: {3107, 4000, 4444, 4674, 10173, 12498},\n",
       "             2965: {373, 1693, 2823, 3607, 4032, 5431, 6433, 8928, 12969},\n",
       "             1036: {338, 3721, 4518, 5273, 5548, 8010, 10080, 10688, 11757},\n",
       "             1960: {1697, 3153, 4349, 5534, 9439, 10399, 11924, 12716},\n",
       "             914: {132, 377, 2479, 3061, 13274, 13350},\n",
       "             1273: {465, 8521, 8642, 9032, 9048, 13011},\n",
       "             1531: {1785, 4448, 6570, 9368, 9915, 10434},\n",
       "             3093: {1097, 2479, 3107, 4444, 4674, 9125, 13274},\n",
       "             1063: {1222, 2660, 3446, 4000, 4674, 6044, 10173},\n",
       "             1917: {979, 1005, 2045, 8972, 9707, 11901},\n",
       "             1829: {3935, 4097, 4409, 5432, 5480, 8804, 12125},\n",
       "             2402: {1011, 1371, 3436, 4297, 6630, 10503, 11398, 11924},\n",
       "             2639: {802, 958, 2038, 2642, 7992, 9294},\n",
       "             2585: {1134, 2592, 3279, 5134, 6837, 12757},\n",
       "             1687: {1126, 2728, 5685, 10724, 11383, 12593},\n",
       "             824: {197,\n",
       "              1267,\n",
       "              1629,\n",
       "              1727,\n",
       "              1739,\n",
       "              2661,\n",
       "              3567,\n",
       "              3934,\n",
       "              4800,\n",
       "              5686,\n",
       "              7164,\n",
       "              7239,\n",
       "              7917,\n",
       "              8086,\n",
       "              9220,\n",
       "              9481,\n",
       "              9835,\n",
       "              10371,\n",
       "              10403,\n",
       "              10828,\n",
       "              11143,\n",
       "              11343,\n",
       "              11565,\n",
       "              12441,\n",
       "              13305},\n",
       "             3388: {1095, 5501, 5542, 6318, 12330, 12421},\n",
       "             1457: {2116, 2307, 3429, 9351, 10210, 13210},\n",
       "             584: {672, 4881, 5654, 8190, 12531, 12955},\n",
       "             405: {2458, 2727, 5437, 7744, 8411, 9031, 10395},\n",
       "             124: {686, 1950, 3902, 4419, 10515, 10543},\n",
       "             263: {132, 874, 2660, 4674, 7039, 13274},\n",
       "             923: {242, 2283, 5766, 7810, 9956, 10556, 12402},\n",
       "             1312: {1957, 2164, 3100, 3307, 6334, 11213},\n",
       "             3043: {2093, 2710, 3556, 4170, 4352, 9037, 11051},\n",
       "             2104: {703, 4510, 4565, 6840, 8958, 9326, 9914},\n",
       "             2182: {454, 2619, 3600, 6493, 9896, 11476},\n",
       "             484: {1896, 4448, 7857, 8190, 10434, 10500},\n",
       "             1160: {570, 926, 2668, 3484, 7088, 9012},\n",
       "             1576: {2382, 8451, 9028, 10961, 11039, 11193},\n",
       "             2303: {1715, 3107, 3446, 4227, 4674, 9125},\n",
       "             1267: {2928, 3843, 4157, 6773, 10038, 10617},\n",
       "             2957: {5428, 6117, 6844, 7242, 7268, 9678, 10234, 11155, 12646},\n",
       "             2275: {2758, 4524, 5262, 6535, 11529, 12015, 13029},\n",
       "             2819: {2626, 4519, 7947, 10734, 11046, 12359},\n",
       "             1323: {4967, 6318, 7071, 11403, 12590, 13356},\n",
       "             3283: {2660, 3446, 4000, 4674, 7154, 13274},\n",
       "             1334: {56, 3405, 3572, 4925, 12202, 12593},\n",
       "             464: {3107, 4444, 4674, 8779, 9125, 10173},\n",
       "             1383: {193,\n",
       "              225,\n",
       "              2154,\n",
       "              2632,\n",
       "              4105,\n",
       "              4959,\n",
       "              5526,\n",
       "              5723,\n",
       "              5911,\n",
       "              6145,\n",
       "              6221,\n",
       "              6559,\n",
       "              6892,\n",
       "              7545,\n",
       "              7777,\n",
       "              8043,\n",
       "              8084,\n",
       "              8471,\n",
       "              8736,\n",
       "              9250,\n",
       "              10216,\n",
       "              11087,\n",
       "              11276,\n",
       "              11483,\n",
       "              11514},\n",
       "             1954: {345, 1896, 3144, 4553, 8299, 9674},\n",
       "             66: {1830, 5818, 10628, 11948, 12273, 12436, 12512},\n",
       "             1938: {2485, 3456, 5890, 6270, 9199, 11344},\n",
       "             863: {377, 2660, 4599, 4674, 8779, 10173, 13274},\n",
       "             3225: {5010, 5869, 7272, 7607, 7725, 12081},\n",
       "             324: {446, 3020, 3774, 3986, 6873, 8478},\n",
       "             2072: {154, 1999, 3552, 10049, 10345, 12442},\n",
       "             3369: {509, 802, 2038, 4407, 10437, 12046},\n",
       "             1122: {1636,\n",
       "              1890,\n",
       "              4326,\n",
       "              5049,\n",
       "              5111,\n",
       "              5262,\n",
       "              5280,\n",
       "              6421,\n",
       "              6806,\n",
       "              10941,\n",
       "              13340,\n",
       "              13343},\n",
       "             1651: {4529, 5345, 7193, 8113, 10269, 13195},\n",
       "             2334: {2458, 5437, 6360, 6658, 7577, 8266, 11752},\n",
       "             1918: {3342, 4448, 8190, 8726, 10500, 12532},\n",
       "             2617: {967, 2458, 5437, 6658, 9416, 12688},\n",
       "             2277: {1865, 5036, 5701, 7788, 8966, 10038, 10208, 10607, 13320},\n",
       "             2645: {6107, 7965, 9078, 9717, 9788, 9790, 10010},\n",
       "             3350: {224, 4277, 6044, 8347, 8779, 10173},\n",
       "             1645: {674, 3866, 4448, 8190, 9802, 10500},\n",
       "             348: {3009, 4500, 7055, 9872, 10138, 11416},\n",
       "             997: {6200, 6593, 7465, 10785, 12312, 13090},\n",
       "             2738: {1575, 3031, 5674, 7178, 10179, 13413},\n",
       "             105: {427, 1896, 2038, 3039, 4967, 12590},\n",
       "             3017: {2223, 3086, 3261, 7414, 9541, 12479},\n",
       "             2647: {2727, 2796, 7692, 8441, 10004, 11752},\n",
       "             1145: {1333, 1826, 4014, 6011, 7038, 7989, 12381},\n",
       "             166: {1544, 1730, 2465, 5437, 6362, 7078},\n",
       "             1227: {1095, 1656, 1896, 5546, 7190, 9357, 11214},\n",
       "             498: {1896, 2038, 5047, 5546, 7190, 8116, 11214},\n",
       "             3075: {132, 377, 3446, 4599, 4674, 7042, 7241, 13274},\n",
       "             311: {1497, 3334, 7660, 12254, 12757, 12841},\n",
       "             1761: {143, 717, 1896, 5632, 8190, 12955},\n",
       "             2466: {144, 333, 3050, 5816, 6539, 7007, 7472},\n",
       "             1316: {965, 3431, 8724, 9829, 10962, 11057},\n",
       "             180: {189, 2866, 3956, 5431, 6975, 9119, 11891, 12705},\n",
       "             468: {486, 7224, 8161, 9360, 11296, 11456},\n",
       "             2610: {1656, 5479, 5546, 6827, 8992, 9217},\n",
       "             3376: {648,\n",
       "              1670,\n",
       "              1896,\n",
       "              4448,\n",
       "              4630,\n",
       "              8190,\n",
       "              9652,\n",
       "              9802,\n",
       "              10434,\n",
       "              10451,\n",
       "              11368,\n",
       "              12586},\n",
       "             3108: {355, 1896, 2853, 8190, 10434, 12586},\n",
       "             1034: {4448, 7132, 8190, 12613},\n",
       "             316: {212, 2480, 3281, 4331, 5660, 7955, 10028},\n",
       "             817: {274,\n",
       "              958,\n",
       "              2816,\n",
       "              5781,\n",
       "              5945,\n",
       "              6922,\n",
       "              9135,\n",
       "              9607,\n",
       "              10409,\n",
       "              12187,\n",
       "              12995,\n",
       "              13381},\n",
       "             3343: {2871, 5061, 5245, 7035, 8783, 11101, 11366},\n",
       "             2133: {1382, 4214, 4359, 4520, 5043, 10350},\n",
       "             1372: {3107, 3446, 4000, 4674, 6343, 9125},\n",
       "             2953: {233,\n",
       "              559,\n",
       "              1896,\n",
       "              1913,\n",
       "              2540,\n",
       "              3308,\n",
       "              4967,\n",
       "              5145,\n",
       "              6318,\n",
       "              6860,\n",
       "              6883,\n",
       "              7387,\n",
       "              8348,\n",
       "              11308,\n",
       "              12142},\n",
       "             2709: {917, 1621, 1736, 6836, 7652, 10060},\n",
       "             1857: {1126, 2236, 6318, 7071, 11403, 11479},\n",
       "             2623: {1529, 1573, 6702, 8939, 11089, 11673},\n",
       "             469: {4312, 4407, 7677, 8332, 8581, 13212},\n",
       "             2947: {482, 2744, 6611, 8940, 9375, 9505},\n",
       "             632: {956,\n",
       "              1265,\n",
       "              1896,\n",
       "              2323,\n",
       "              2781,\n",
       "              2947,\n",
       "              4967,\n",
       "              6192,\n",
       "              6318,\n",
       "              7071,\n",
       "              8190,\n",
       "              8603,\n",
       "              9287,\n",
       "              9430,\n",
       "              10682,\n",
       "              11403},\n",
       "             625: {176, 2886, 4458, 5030, 11085},\n",
       "             501: {2885, 3797, 7275, 7636, 8746, 11616, 13084},\n",
       "             2136: {4158, 10178, 10379, 11454, 11744, 12950},\n",
       "             1103: {1127, 1640, 2585, 6678, 7343, 7672, 7978, 11431, 12789},\n",
       "             1237: {1060, 3734, 5056, 6150, 6498, 7740, 8994},\n",
       "             1512: {1081, 3335, 4929, 6415, 6633, 10036},\n",
       "             2195: {790, 3871, 5607, 6987, 10561, 10926},\n",
       "             1393: {1891, 3357, 3529, 4443, 5496, 7807, 12744},\n",
       "             1870: {186, 2631, 2975, 4297, 4584, 8711, 9456},\n",
       "             1243: {1640, 2099, 6430, 8252, 8631, 11535, 12774},\n",
       "             185: {2252, 3862, 6642, 7868},\n",
       "             1028: {3107, 4674, 9125, 12869, 13274},\n",
       "             566: {665, 2231, 8735, 9596, 12012, 12527},\n",
       "             627: {427, 1656, 1896, 4559, 11959, 13212},\n",
       "             1922: {70, 8470, 9612, 10235, 11852, 12533},\n",
       "             1090: {3107, 4000, 4674, 8779, 9125, 10173},\n",
       "             136: {4188, 4235, 6721, 7412, 9259, 11071, 12192},\n",
       "             139: {1230, 1703, 4030, 4421, 6081, 7703, 10123},\n",
       "             2832: {614, 1896, 3070, 4448, 7540, 8190, 10434, 11251},\n",
       "             46: {1944, 4015, 4080, 8520, 13079, 13163},\n",
       "             1941: {424, 2775, 5054, 5280, 6012, 11342},\n",
       "             1536: {441, 1513, 2248, 2520, 8039, 9077, 10248, 10914},\n",
       "             2121: {1120, 1383, 2454, 6263, 7060, 8724, 9433, 10372},\n",
       "             1358: {2371, 4307, 5543, 9660, 11876, 13013},\n",
       "             900: {56, 1896, 4597, 8190, 9068, 11251},\n",
       "             3272: {5990, 6111, 6713, 7677, 7901, 10720},\n",
       "             2646: {2621, 3053, 11997, 12083},\n",
       "             2398: {709, 2675, 2770, 3539, 4531, 9571, 9975},\n",
       "             2063: {13, 7168, 7910, 9382, 10243, 13350},\n",
       "             2626: {1694, 5418, 6272, 8686, 10205, 10225},\n",
       "             1347: {1896, 2204, 3334, 5561, 7190, 8190},\n",
       "             630: {132, 1715, 4000, 4227, 4674, 7353},\n",
       "             2399: {377, 3446, 4000, 4599, 4674, 12869, 13274},\n",
       "             2305: {192, 1904, 2401, 4055, 6656, 13409},\n",
       "             2809: {1242, 1855, 5863, 10492, 12452},\n",
       "             895: {631, 1896, 2578, 3335, 9913, 10434, 11064, 12696},\n",
       "             1551: {1222, 1715, 3107, 4674, 6044, 8779, 10173},\n",
       "             3010: {293, 4108, 4131, 4803, 5403, 6265, 7345, 11353},\n",
       "             383: {1217, 3228, 3369, 4407, 8200, 9959, 10419, 10588, 12491},\n",
       "             2058: {78, 7189, 8696, 8737, 8861, 9055, 11925},\n",
       "             2400: {1896, 3386, 5866, 8190, 10131, 11358, 11690, 12512, 13144},\n",
       "             2060: {328, 6062, 10318, 11777},\n",
       "             1004: {1929, 2123, 5262, 5825, 8875, 11323},\n",
       "             589: {706, 1126, 8764, 8939, 9217, 10607, 12803},\n",
       "             1716: {2187, 3360, 3832, 5448, 8209, 9829},\n",
       "             830: {2616, 3331, 5400, 8121, 9654, 10510, 12143},\n",
       "             219: {8200, 10620, 12491, 12744, 12792, 13075},\n",
       "             2306: {1896, 3871, 5607, 6318, 8190, 11403},\n",
       "             2050: {56, 1569, 1896, 3179, 3211, 6822},\n",
       "             3094: {132, 874, 3107, 4674, 6044, 9125, 10169},\n",
       "             2370: {711, 1266, 4407, 5414, 8150, 8200},\n",
       "             1762: {1383, 6344, 6653, 8851, 10023, 10245},\n",
       "             403: {1222, 3446, 4674, 7241, 8779, 10173},\n",
       "             922: {802, 958, 3004, 6399, 6967, 12354},\n",
       "             669: {1, 1650, 3982, 4425, 4728, 5025},\n",
       "             2225: {1898, 2001, 3468, 8377, 13295, 13404},\n",
       "             658: {44, 2117, 6042, 7256, 9302, 12821},\n",
       "             292: {4761, 4797, 8487, 9639, 10067, 10942, 12958},\n",
       "             1786: {1567, 2331, 2600, 10125, 10312, 10441},\n",
       "             3224: {1084, 3680, 3944, 5933, 7415, 9655},\n",
       "             2196: {679, 1896, 3871, 4967, 5607, 6318, 7071, 8190, 11403},\n",
       "             3076: {1420, 1656, 1896, 4984, 5546, 7138, 7190, 11214},\n",
       "             3383: {668, 843, 7956, 9435, 11951, 12385},\n",
       "             1748: {2265, 4071, 4646, 5414, 5703, 7857, 8200, 11589, 12593},\n",
       "             1437: {2038, 3407, 4407, 6468},\n",
       "             1858: {1842, 2068, 4926, 6451, 8098, 9938},\n",
       "             1726: {2408, 5064, 5729, 9030, 11668, 13075},\n",
       "             536: {3871, 8190, 8549, 8603, 10179, 12590},\n",
       "             2359: {1896, 2032, 2367, 5546, 5830, 11214},\n",
       "             2837: {177, 7083, 9900, 10516, 11707, 13056},\n",
       "             1225: {1896, 4334, 7190, 7461, 8190, 11614},\n",
       "             862: {132, 2660, 3446, 4674, 8779, 13274},\n",
       "             1179: {2456, 4867, 8135, 9937, 12504, 12543, 13386},\n",
       "             548: {1855, 4357, 4575, 9177, 9338, 12864},\n",
       "             424: {1982, 2431, 3382, 3683, 5469, 12701},\n",
       "             1462: {186, 263, 4297, 6835, 7403, 8285},\n",
       "             3337: {1003, 4480, 7516, 8179, 9817, 10344},\n",
       "             3127: {180,\n",
       "              992,\n",
       "              2170,\n",
       "              2173,\n",
       "              2917,\n",
       "              3131,\n",
       "              3518,\n",
       "              3660,\n",
       "              4658,\n",
       "              5206,\n",
       "              5914,\n",
       "              6459,\n",
       "              6957,\n",
       "              7108,\n",
       "              7155,\n",
       "              8756,\n",
       "              9381,\n",
       "              9593,\n",
       "              9730,\n",
       "              10033,\n",
       "              10597,\n",
       "              11356,\n",
       "              11516,\n",
       "              12073,\n",
       "              12178},\n",
       "             198: {1127, 1231, 2774, 7991, 9370, 11361},\n",
       "             2693: {432, 8249, 8259, 8458, 9997, 12742},\n",
       "             2478: {870,\n",
       "              1896,\n",
       "              2820,\n",
       "              3467,\n",
       "              3717,\n",
       "              4448,\n",
       "              4929,\n",
       "              5861,\n",
       "              6100,\n",
       "              6884,\n",
       "              8190,\n",
       "              10451,\n",
       "              10500,\n",
       "              12071},\n",
       "             1690: {5809, 6619, 7887, 10087, 12452, 12690},\n",
       "             1261: {385, 2822, 3603, 10955, 12544, 12926},\n",
       "             1115: {3107, 4444, 4674, 7241, 9125, 13274},\n",
       "             1106: {999, 1640, 2020, 4097, 5486, 5541, 13247},\n",
       "             929: {957,\n",
       "              1583,\n",
       "              2038,\n",
       "              3144,\n",
       "              3854,\n",
       "              4089,\n",
       "              5159,\n",
       "              5944,\n",
       "              7796,\n",
       "              10351,\n",
       "              12687},\n",
       "             240: {1730, 2458, 2727, 5437, 5952, 11752},\n",
       "             3389: {3834, 10029, 10162, 10893, 12037, 12589},\n",
       "             1102: {1677, 2785, 3694, 6878, 7189, 9944},\n",
       "             2748: {5486, 6335, 7043, 7587, 11935, 13152},\n",
       "             792: {224, 2287, 4277, 6044, 7650, 10173, 12066},\n",
       "             2185: {1095,\n",
       "              1656,\n",
       "              1896,\n",
       "              3377,\n",
       "              4722,\n",
       "              5259,\n",
       "              5546,\n",
       "              7190,\n",
       "              7401,\n",
       "              8624,\n",
       "              8992,\n",
       "              11214,\n",
       "              13339},\n",
       "             64: {1824, 6662, 8561, 11639, 12410, 13131},\n",
       "             257: {601, 802, 2038, 3407, 4312, 8200},\n",
       "             1210: {462, 6660, 7429, 8206, 10863, 10900},\n",
       "             1096: {3541, 5112, 6206, 9406, 9829, 10962},\n",
       "             3298: {5340, 8489, 9225, 9443, 9792},\n",
       "             2381: {512, 4026, 4254, 9183, 11841, 13270},\n",
       "             2377: {377, 2660, 3446, 4000, 4674, 7353, 8779, 10173},\n",
       "             1657: {1896, 2953, 4984, 5546, 7190, 7882, 11214},\n",
       "             3342: {190,\n",
       "              248,\n",
       "              737,\n",
       "              3103,\n",
       "              3365,\n",
       "              5393,\n",
       "              6536,\n",
       "              6638,\n",
       "              11916,\n",
       "              12740,\n",
       "              13255},\n",
       "             2325: {377, 3446, 4000, 4674, 8779, 10173},\n",
       "             248: {1139, 5001, 7844, 8024, 8544, 10458},\n",
       "             1703: {1711, 8200, 11240, 11306, 12012, 12846, 13291},\n",
       "             1655: {940, 4187, 4514, 4762, 7483, 12340},\n",
       "             1411: {852,\n",
       "              1243,\n",
       "              4020,\n",
       "              4393,\n",
       "              5627,\n",
       "              5667,\n",
       "              6167,\n",
       "              6760,\n",
       "              7122,\n",
       "              7655,\n",
       "              7766,\n",
       "              8419,\n",
       "              9292,\n",
       "              10025,\n",
       "              10309,\n",
       "              12072},\n",
       "             547: {1790, 2025, 3718, 6699, 9679, 10126},\n",
       "             2612: {1800, 2429, 6699, 8841, 9912, 11764, 12757},\n",
       "             1293: {1127, 1194, 1832, 2402, 2774, 8322},\n",
       "             1824: {777, 3006, 7202, 11245, 11465, 13322},\n",
       "             1955: {1583, 5676, 7887, 10686, 12574, 12689},\n",
       "             776: {1896, 4448, 8190, 8777, 10434, 10500},\n",
       "             2632: {1896, 2578, 3163, 4791, 10434},\n",
       "             2492: {803, 899, 1384, 1756, 3858, 8655, 8772, 10925, 11970},\n",
       "             3370: {1896, 4448, 7190, 8190, 10434, 10451},\n",
       "             70: {505,\n",
       "              1355,\n",
       "              1468,\n",
       "              2121,\n",
       "              2364,\n",
       "              2795,\n",
       "              3063,\n",
       "              3563,\n",
       "              3738,\n",
       "              3987,\n",
       "              5100,\n",
       "              5374,\n",
       "              6134,\n",
       "              6723,\n",
       "              7271,\n",
       "              8004,\n",
       "              8511,\n",
       "              8646,\n",
       "              9082,\n",
       "              9117,\n",
       "              9132,\n",
       "              9396,\n",
       "              10073,\n",
       "              10536,\n",
       "              11206,\n",
       "              11346,\n",
       "              11827,\n",
       "              11846,\n",
       "              12269,\n",
       "              12890,\n",
       "              12956,\n",
       "              13264},\n",
       "             1521: {3300, 4805, 5702, 8521, 9032, 10820},\n",
       "             1125: {1188, 3430, 4036, 7649, 7698, 11830},\n",
       "             847: {5414, 8394, 9674, 11594, 11710, 12593},\n",
       "             2197: {346, 1224, 6312, 7945, 11594, 12477},\n",
       "             238: {1656, 1896, 5546, 7190, 9674, 11214},\n",
       "             1488: {201, 5588, 5781, 10038, 11594},\n",
       "             2540: {2458, 5437, 6469, 7078, 7577, 11752},\n",
       "             3317: {541, 2176, 3199, 4345, 7846, 10111},\n",
       "             3031: {346, 5944, 7107, 8772, 13127, 13248},\n",
       "             3288: {56, 2070, 6980, 7190, 7653, 13121},\n",
       "             2451: {1603, 5319, 5455, 6733, 7399, 11995},\n",
       "             2080: {7980, 12896, 12979, 13287},\n",
       "             157: {1715, 3107, 3524, 4674, 9125, 10173},\n",
       "             1963: {5448, 5546, 5830, 6998, 7401, 10279, 11214},\n",
       "             404: {730, 3966, 7327, 11387},\n",
       "             1500: {3613, 4300, 4671, 6153, 8224, 11233},\n",
       "             2929: {1371, 2602, 4293, 4297, 5535, 6630},\n",
       "             3115: {1896, 4448, 7190, 8190, 10434, 12500},\n",
       "             1577: {419, 1382, 7474, 7887, 11301, 11936},\n",
       "             83: {2287, 5797, 6044, 7650, 9446, 12514},\n",
       "             785: {227, 3210, 7887, 9345, 12728, 13039},\n",
       "             2248: {874, 1240, 2660, 4000, 4599, 4674, 5166, 13274},\n",
       "             3210: {413, 1335, 1549, 4157, 10038, 10717, 10861},\n",
       "             2074: {1770, 2004, 3277, 4743, 6959, 8449},\n",
       "             102: {2660, 4378, 4674, 8779, 10173, 13274},\n",
       "             2119: {1101, 1896, 3580, 4451, 5546, 7190, 8624, 11214},\n",
       "             1171: {1896, 4448, 7835, 8190, 10434, 12384},\n",
       "             1977: {621,\n",
       "              708,\n",
       "              1800,\n",
       "              3334,\n",
       "              3809,\n",
       "              5939,\n",
       "              7389,\n",
       "              7669,\n",
       "              7956,\n",
       "              11316,\n",
       "              12757},\n",
       "             2983: {3107, 4444, 4674, 6044, 8779, 10173},\n",
       "             1135: {3579,\n",
       "              4136,\n",
       "              7556,\n",
       "              7720,\n",
       "              7887,\n",
       "              8995,\n",
       "              9843,\n",
       "              9959,\n",
       "              10722,\n",
       "              10925,\n",
       "              11508,\n",
       "              12400},\n",
       "             3174: {1116, 1946, 6469, 7268, 9416, 10234, 13168},\n",
       "             1195: {3873, 3874, 5095, 5858, 7990, 12529},\n",
       "             1569: {802, 1583, 4312, 4407, 8200, 8557, 12593},\n",
       "             1588: {51, 123, 3427, 3620, 5924, 6517, 11248},\n",
       "             2184: {29, 426, 1916, 2742, 4904, 8154, 12271},\n",
       "             358: {4162, 4438, 4439, 4673, 4784, 5894, 8017, 9675, 11379},\n",
       "             1994: {2660, 4674, 6044, 7154, 8779, 10173},\n",
       "             2331: {928, 2509, 3859, 8832, 9998, 12058, 13027},\n",
       "             433: {427, 2367, 4967, 5027, 6318, 12593},\n",
       "             3084: {132, 377, 1222, 4227, 4674, 10173},\n",
       "             432: {62, 433, 4289, 7608, 9402, 11772},\n",
       "             3327: {958, 9761, 10409, 10540, 12239, 12354},\n",
       "             2318: {4066, 4413, 4534, 8423, 9025, 11158, 11187, 12290},\n",
       "             3013: {5383, 6895, 7601, 7966, 8510, 8941},\n",
       "             711: {1956,\n",
       "              3875,\n",
       "              4295,\n",
       "              6224,\n",
       "              6497,\n",
       "              7305,\n",
       "              7385,\n",
       "              9488,\n",
       "              10193,\n",
       "              10892},\n",
       "             1933: {143, 1896, 2701, 4448, 8190, 10434},\n",
       "             1527: {1383, 1896, 4448, 8190, 9089, 10434},\n",
       "             1116: {1040, 6409, 6541, 8589, 9581, 11881},\n",
       "             605: {7095, 8015, 10531, 11550, 11737, 13319},\n",
       "             2822: {710, 1539, 5214, 5841, 6687, 8972},\n",
       "             2432: {90, 4885, 5014, 9459, 9886, 10791},\n",
       "             3314: {684, 1730, 2863, 4190, 7280, 11752},\n",
       "             564: {3886, 5081, 6254, 9007, 10382, 12253},\n",
       "             3310: {431, 982, 7160, 7721, 11855, 12757},\n",
       "             2698: {276,\n",
       "              1089,\n",
       "              1430,\n",
       "              2096,\n",
       "              9548,\n",
       "              10683,\n",
       "              10929,\n",
       "              12689,\n",
       "              12838,\n",
       "              13177},\n",
       "             2589: {1853, 10821, 10982, 12384, 12591, 12757},\n",
       "             1007: {301, 1583, 2038, 3394, 4389, 4987, 5286, 8377},\n",
       "             3077: {2100, 4297, 7287, 7521, 9439, 11584},\n",
       "             2839: {1896,\n",
       "              3822,\n",
       "              4967,\n",
       "              5563,\n",
       "              5607,\n",
       "              7071,\n",
       "              7498,\n",
       "              7622,\n",
       "              8190,\n",
       "              12590,\n",
       "              13356},\n",
       "             2272: {267, 1676, 2308, 3465, 11969, 12557},\n",
       "             573: {3593, 5119, 5321, 7313, 7755, 8224, 12652, 13347},\n",
       "             3000: {802, 5286, 8200, 10419, 12239},\n",
       "             2304: {21, 1069, 4495, 5102, 7332, 7689},\n",
       "             1137: {703, 1896, 4915, 6263, 6840, 7190, 8587},\n",
       "             3186: {446, 6192, 9287, 9430, 11144, 11818},\n",
       "             31: {624, 2689, 4448, 7477, 8190, 10500, 11625},\n",
       "             3178: {2087, 2672, 4146, 5456, 5703, 12863},\n",
       "             1695: {374, 1896, 2729, 5546, 7190, 11214},\n",
       "             672: {918,\n",
       "              1234,\n",
       "              2809,\n",
       "              2963,\n",
       "              3871,\n",
       "              4333,\n",
       "              5318,\n",
       "              5607,\n",
       "              5712,\n",
       "              6363,\n",
       "              6772,\n",
       "              10926,\n",
       "              13092},\n",
       "             2587: {663, 1113, 4439, 4811, 6141, 7951, 10693},\n",
       "             1066: {124,\n",
       "              2088,\n",
       "              2428,\n",
       "              2500,\n",
       "              3492,\n",
       "              3883,\n",
       "              4053,\n",
       "              4307,\n",
       "              4391,\n",
       "              4510,\n",
       "              4562,\n",
       "              5451,\n",
       "              5940,\n",
       "              6097,\n",
       "              6104,\n",
       "              6643,\n",
       "              8003,\n",
       "              9038,\n",
       "              9210,\n",
       "              9260,\n",
       "              9397,\n",
       "              9598,\n",
       "              10471,\n",
       "              11877,\n",
       "              11912,\n",
       "              12323,\n",
       "              12347,\n",
       "              12552},\n",
       "             1518: {1530, 2629, 3265, 4371, 10261, 10867},\n",
       "             917: {809, 1531, 2645, 5845, 6573, 6964, 10439},\n",
       "             3119: {322, 9435, 10297, 10571, 10653, 10885},\n",
       "             2245: {568, 703, 898, 2496, 4488, 6840, 7111, 11585},\n",
       "             1505: {5535, 6181, 6630, 11345, 11794, 12440},\n",
       "             2319: {5944, 7887, 7910, 8223, 9548, 10202},\n",
       "             489: {3673, 5756, 7888, 8100, 8992, 12103, 12849},\n",
       "             2209: {1800, 5453, 6533, 7956, 9023, 12757},\n",
       "             2797: {651, 3545, 8015, 9031, 11752, 12646},\n",
       "             2187: {1103, 1896, 3614, 6860, 7454, 8190},\n",
       "             205: {2727, 7078, 9008, 9416, 10004, 11752},\n",
       "             320: {1896, 2689, 4448, 4838, 8190, 10500},\n",
       "             722: {1442, 3522, 5775, 9099, 11249, 12928},\n",
       "             36: {2047, 2240, 6877, 8300, 10357, 11981},\n",
       "             2488: {3228, 5414, 5501, 9863, 12326, 12593},\n",
       "             1352: {209, 2020, 3591, 5875, 8201, 12227},\n",
       "             940: {1896, 3717, 4448, 6884, 8190, 10434, 10500},\n",
       "             2029: {733,\n",
       "              1425,\n",
       "              1741,\n",
       "              1774,\n",
       "              2827,\n",
       "              3506,\n",
       "              3642,\n",
       "              5002,\n",
       "              7198,\n",
       "              7509,\n",
       "              7873,\n",
       "              9400,\n",
       "              9508,\n",
       "              9635,\n",
       "              10015,\n",
       "              10768,\n",
       "              11656,\n",
       "              11759,\n",
       "              12406,\n",
       "              12429},\n",
       "             2951: {1365, 2641, 3039, 5682, 12436, 12782},\n",
       "             3234: {1147, 1431, 2870, 5196, 7365, 8464},\n",
       "             2920: {1896,\n",
       "              3871,\n",
       "              4967,\n",
       "              5607,\n",
       "              6318,\n",
       "              7071,\n",
       "              7914,\n",
       "              8190,\n",
       "              10179,\n",
       "              11403},\n",
       "             1429: {862, 1896, 3334, 3684, 4448, 7190, 8190, 10434, 10500},\n",
       "             147: {1896, 1899, 2701, 3334, 7190, 8190, 10343, 12272},\n",
       "             975: {3888, 5093, 5209, 6169, 6799, 10180, 10265},\n",
       "             1238: {2660, 3107, 3446, 4674, 7241, 8779, 10173},\n",
       "             2269: {3334, 4361, 8148, 9015, 9059, 10568, 12272, 12757},\n",
       "             2442: {329, 1896, 4448, 7190, 8190, 10434, 10500, 12185},\n",
       "             1391: {158, 1583, 7887, 12108},\n",
       "             1878: {3107, 3446, 4444, 4674, 8779, 10173},\n",
       "             814: {1485, 2408, 5414, 11695, 12239, 12590},\n",
       "             2405: {132, 2660, 3446, 4674, 7241, 10173},\n",
       "             1883: {1371, 4293, 4297, 5535, 6305, 9439},\n",
       "             977: {905, 968, 7972, 11836, 12202, 13198},\n",
       "             3066: {514, 3003, 3236, 4674, 6929, 8828, 9386, 13235},\n",
       "             2475: {1707, 2767, 3218, 10417, 11068, 13253},\n",
       "             3040: {1561,\n",
       "              2858,\n",
       "              3239,\n",
       "              5826,\n",
       "              7125,\n",
       "              9831,\n",
       "              9929,\n",
       "              11778,\n",
       "              12100,\n",
       "              12675,\n",
       "              12735,\n",
       "              13132},\n",
       "             87: {3810, 3889, 5683, 9725, 11053, 12423},\n",
       "             2914: {1929, 2123, 5104, 6793, 7834, 8881},\n",
       "             1920: {651, 6109, 6924, 11752, 11806, 12852},\n",
       "             3148: {1288,\n",
       "              1733,\n",
       "              1870,\n",
       "              2066,\n",
       "              5094,\n",
       "              5326,\n",
       "              5339,\n",
       "              5468,\n",
       "              6824,\n",
       "              7687,\n",
       "              8695,\n",
       "              9493},\n",
       "             1374: {1308, 1896, 6981, 9864, 11606},\n",
       "             2338: {377, 3107, 4444, 4674, 8779, 10173},\n",
       "             795: {1130, 1386, 2732, 4999, 8190, 9882, 11886},\n",
       "             2502: {1371, 1671, 4297, 5534, 7287, 8711, 11584},\n",
       "             884: {1126, 2601, 4312, 4407, 9030, 11383, 12491, 12744, 13075},\n",
       "             667: {54, 274, 3091, 3972, 4038, 7792, 11357},\n",
       "             2264: {493,\n",
       "              1643,\n",
       "              2900,\n",
       "              3983,\n",
       "              5010,\n",
       "              5551,\n",
       "              8093,\n",
       "              8132,\n",
       "              8516,\n",
       "              9844,\n",
       "              12270,\n",
       "              12623},\n",
       "             616: {1082,\n",
       "              1896,\n",
       "              4448,\n",
       "              7190,\n",
       "              7494,\n",
       "              8190,\n",
       "              9526,\n",
       "              9915,\n",
       "              10434,\n",
       "              10500},\n",
       "             3300: {504, 1618, 4890, 8360, 9786, 11203},\n",
       "             1082: {94, 705, 885, 2930, 3361, 6426},\n",
       "             1523: {463, 703, 4177, 6903, 7501, 13187},\n",
       "             2970: {1371, 4297, 7287, 7521, 11584},\n",
       "             886: {1172, 1383, 3719, 7169, 7235, 7701},\n",
       "             700: {347, 943, 1656, 3871, 4360, 7888, 8899, 10639, 11403},\n",
       "             981: {4978, 6117, 6759, 7141, 7565, 10463},\n",
       "             1592: {3027, 3981, 5316, 6192, 6326, 7183, 9430, 11704, 13128},\n",
       "             2160: {716, 1606, 2077, 4831, 9489, 11637},\n",
       "             705: {51,\n",
       "              386,\n",
       "              492,\n",
       "              572,\n",
       "              3427,\n",
       "              3620,\n",
       "              4385,\n",
       "              5924,\n",
       "              6255,\n",
       "              6517,\n",
       "              8494,\n",
       "              9035,\n",
       "              10883,\n",
       "              11248,\n",
       "              11329,\n",
       "              12148},\n",
       "             500: {729, 1597, 4376, 4692, 8099, 12410},\n",
       "             3291: {3157, 4000, 4674, 7039, 7290, 13274},\n",
       "             1681: {13, 7910, 8200, 8253, 8494, 8870, 9382},\n",
       "             2925: {1896, 3845, 3962, 5318, 5866, 7190, 8190, 9290, 10435},\n",
       "             2720: {876, 1117, 6105, 6151, 12172, 12757},\n",
       "             2554: {3119, 7243, 7329, 8118, 9836, 12244},\n",
       "             1382: {275, 658, 1265, 3202, 7474, 12416},\n",
       "             2820: {590, 3855, 3908, 6639, 7474, 7792},\n",
       "             2563: {1135, 2977, 4674, 5358, 6044, 10173},\n",
       "             2775: {556, 4711, 7003, 7259, 8732},\n",
       "             93: {1365, 4218, 5976, 6281, 7208, 7714, 11515},\n",
       "             1968: {382,\n",
       "              1283,\n",
       "              2571,\n",
       "              3667,\n",
       "              5944,\n",
       "              8377,\n",
       "              8389,\n",
       "              10949,\n",
       "              11523,\n",
       "              12214},\n",
       "             623: {1896, 1899, 3041, 6578, 7190, 8190, 11012},\n",
       "             235: {2072, 8538, 9241, 10158, 12198, 12721},\n",
       "             2417: {1834, 3335, 3489, 7006, 7190, 7653, 12379},\n",
       "             620: {1011, 5534, 7946, 9439, 9919, 11924},\n",
       "             174: {2797, 5101, 6000, 7243, 9308, 9906},\n",
       "             2938: {592,\n",
       "              657,\n",
       "              2774,\n",
       "              3900,\n",
       "              3980,\n",
       "              4429,\n",
       "              4965,\n",
       "              10325,\n",
       "              10402,\n",
       "              11688,\n",
       "              12154,\n",
       "              12880},\n",
       "             2892: {2199, 4111, 4116, 4159, 8857, 11536, 12603},\n",
       "             132: {427, 2571, 3039, 3822, 6318, 11403},\n",
       "             729: {276, 1933, 2572, 2873, 8649, 12239, 13350},\n",
       "             2062: {5577, 7433, 10760, 10816, 11234, 13070},\n",
       "             2324: {795, 4428, 5448, 5709, 7819, 11513},\n",
       "             2438: {377, 3107, 4444, 4674, 7353, 10173},\n",
       "             1792: {8458, 8771, 10631, 11394, 13365},\n",
       "             346: {2622, 3066, 5556, 6713, 7887, 11870, 13315},\n",
       "             3078: {172, 2031, 3247, 6635, 7639, 8057, 9629},\n",
       "             1420: {2606, 2667, 2972, 3099, 5892, 7076},\n",
       "             3059: {1715, 3107, 4674, 8779, 9125, 10173},\n",
       "             1076: {6802, 6821, 7142, 8569, 9650, 11592},\n",
       "             2192: {1619,\n",
       "              1917,\n",
       "              2390,\n",
       "              3887,\n",
       "              4641,\n",
       "              4729,\n",
       "              7324,\n",
       "              7891,\n",
       "              7896,\n",
       "              8748,\n",
       "              10376,\n",
       "              11331},\n",
       "             3029: {1383, 1896, 4448, 8190, 10434, 10500},\n",
       "             2992: {18, 1801, 3890, 5915, 11264, 11382, 13342},\n",
       "             2528: {377, 1383, 1599, 4674, 9472},\n",
       "             1331: {2038, 4143, 5414, 6808, 8200, 10107},\n",
       "             2469: {1896, 3334, 4448, 8190, 9506, 10451, 12071},\n",
       "             3085: {1143, 2813, 3489, 6369, 7190, 8064, 10505},\n",
       "             119: {1629, 2984, 3415, 6800, 12332},\n",
       "             2388: {320, 1360, 3345, 4811, 6141, 6804, 7951},\n",
       "             2073: {377, 2287, 5797, 7650, 9472, 12514},\n",
       "             559: {3107, 3446, 4000, 4674, 9125, 13274},\n",
       "             1774: {131, 6192, 6326, 7699, 8630, 8836, 9270, 9430, 11144},\n",
       "             1018: {452, 1403, 1648, 7772, 7869, 8550},\n",
       "             3015: {1797, 2734, 3300, 4087, 9258},\n",
       "             1470: {1855, 3602, 8724, 10270, 12363, 12452},\n",
       "             2740: {1863, 4277, 4444, 6044, 7675, 10173},\n",
       "             2507: {7228, 8622, 9393, 11744, 12632, 12950},\n",
       "             94: {4779, 8690, 9754, 10128, 11882, 13174},\n",
       "             71: {387, 537, 661, 3072, 5328, 6590},\n",
       "             941: {1896,\n",
       "              3698,\n",
       "              3971,\n",
       "              4081,\n",
       "              4204,\n",
       "              4676,\n",
       "              5276,\n",
       "              5546,\n",
       "              7963,\n",
       "              11021,\n",
       "              11598,\n",
       "              11666,\n",
       "              12330},\n",
       "             3223: {3107, 4000, 4674, 8779, 9125, 10173},\n",
       "             1911: {1347, 1480, 1534, 1913, 3822, 7677, 11876},\n",
       "             1946: {143, 461, 1740, 1916, 2592, 3190, 12757},\n",
       "             200: {4537, 5763, 7267, 11205, 12620, 12647},\n",
       "             1780: {159, 3015, 3580, 4942, 6318, 8628, 9167, 9823, 11403},\n",
       "             2835: {14, 534, 1107, 3142, 11821, 13297},\n",
       "             2861: {685, 3936, 6468, 11673, 11966, 13075},\n",
       "             3068: {3446, 4674, 7353, 10169, 10173, 13274},\n",
       "             2831: {1137, 2936, 4196, 6394, 8193, 11259},\n",
       "             706: {220,\n",
       "              425,\n",
       "              5969,\n",
       "              6516,\n",
       "              7563,\n",
       "              8027,\n",
       "              9236,\n",
       "              9599,\n",
       "              9945,\n",
       "              11095,\n",
       "              11260,\n",
       "              11341},\n",
       "             1206: {3309, 4095, 4166, 7200, 9052, 12713},\n",
       "             3155: {2660, 3446, 4000, 4444, 4674, 8779, 10173},\n",
       "             2808: {4967, 6318, 7071, 8190, 10318, 10671, 11403},\n",
       "             2878: {3121, 6193, 7970, 8654, 11262, 11712},\n",
       "             3316: {377, 3107, 3157, 4674, 8779, 10173},\n",
       "             1181: {2650, 5218, 6317, 7330, 8109, 10369},\n",
       "             2723: {6885, 8014, 8291, 10927},\n",
       "             380: {2727, 3829, 5763, 9311, 10664, 10849},\n",
       "             1510: {4967, 6468, 7059, 9167, 9429, 12736, 13212},\n",
       "             2019: {2128, 2717, 5262, 8903, 10016, 12391, 12524, 13343},\n",
       "             2783: {5641, 7575, 8178, 10267, 10844, 13344},\n",
       "             3276: {2406, 3319, 3770, 6985, 9980, 10330},\n",
       "             1318: {1371, 4297, 6630, 7287, 7521, 8711, 11252},\n",
       "             3311: {392, 2147, 5432, 5480, 5785, 6387, 8417},\n",
       "             61: {2320, 3102, 6179, 7001, 11873, 12057},\n",
       "             1212: {447, 4052, 4228, 4563, 8452, 12340},\n",
       "             1638: {1786, 1809, 4521, 5010, 12638, 13111},\n",
       "             3023: {322,\n",
       "              1713,\n",
       "              2532,\n",
       "              2638,\n",
       "              4510,\n",
       "              6097,\n",
       "              6840,\n",
       "              8349,\n",
       "              11453,\n",
       "              11547},\n",
       "             815: {274, 1583, 2304, 4553, 4707, 5335, 9761},\n",
       "             949: {950, 8772, 8967, 9167, 10671, 11371, 12007},\n",
       "             2671: {417, 933, 4677, 5542, 7153, 8548, 8992, 11149, 12330},\n",
       "             1749: {204,\n",
       "              1414,\n",
       "              1896,\n",
       "              1988,\n",
       "              3594,\n",
       "              4407,\n",
       "              5413,\n",
       "              5945,\n",
       "              6085,\n",
       "              7732,\n",
       "              8377,\n",
       "              8581,\n",
       "              8587,\n",
       "              10372,\n",
       "              11984,\n",
       "              12063,\n",
       "              12187},\n",
       "             1828: {1222, 3446, 4000, 4674, 6044, 10173},\n",
       "             1769: {3214, 4235, 6721, 11071, 12666},\n",
       "             3218: {1715, 3446, 4000, 4674, 8347, 8779, 10173},\n",
       "             1599: {1583, 3503, 4389, 4407, 5220, 12963},\n",
       "             2962: {80,\n",
       "              1337,\n",
       "              3688,\n",
       "              5829,\n",
       "              6641,\n",
       "              6738,\n",
       "              8917,\n",
       "              9322,\n",
       "              11026,\n",
       "              11662},\n",
       "             357: {1796, 3362, 3843, 5836, 6287, 6663, 10038, 11367, 12477},\n",
       "             1722: {1896, 3871, 3999, 5607, 6298, 7190, 8190, 11472},\n",
       "             2565: {132, 3446, 4000, 4599, 4674, 7241, 7353},\n",
       "             1993: {1171, 1629, 1633, 3115, 7187, 9695},\n",
       "             932: {1700, 2824, 4266, 5817, 9633, 12445},\n",
       "             323: {5298, 5615, 8267, 12054, 13149},\n",
       "             1574: {5148, 9046, 12200, 12611, 13137, 13387},\n",
       "             2843: {532, 1130, 1313, 3256, 6499, 6578, 12120},\n",
       "             2582: {2162, 3446, 4444, 4674, 8779, 10173},\n",
       "             431: {2092, 3334, 4448, 8190, 9479, 11064, 11603},\n",
       "             1797: {609, 1896, 7436, 10190, 11566, 11960, 13383, 13386},\n",
       "             919: {9, 792, 872, 2721, 7013, 9408, 11221, 11354},\n",
       "             440: {2287, 4277, 7650, 8347, 8779, 10173},\n",
       "             2852: {816, 5291, 6395, 8913},\n",
       "             ...})"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eventsForUser"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       ..., \n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "userEventScores.toarray()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       " (2654, 3283),\n",
       " (2396, 1767),\n",
       " (3299, 974),\n",
       " (774, 2798),\n",
       " (2970, 1842),\n",
       " (241, 1298),\n",
       " (2859, 941),\n",
       " (3116, 403),\n",
       " (2591, 498),\n",
       " (653, 911),\n",
       " (2603, 2300),\n",
       " (2854, 864),\n",
       " (3352, 730),\n",
       " (1079, 1225),\n",
       " (1667, 3029),\n",
       " (2374, 1374),\n",
       " (3354, 360),\n",
       " ...}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "uniqueUserPairs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#训练集和测试集中出现的用户数目和事件数目远小于users.csv出现的用户数和events.csv出现的事件数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       ..., \n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "userEventScores.toarray()"
   ]
  }
 ],
 "metadata": {
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